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Leonardo numbers are also known as the Leonardo series.

The Leonardo numbers are a sequence of numbers defined by:

       L(0) = 1                                          [1^st equation]  
       L(1) = 1                                          [2^nd equation]  
       L(n) = L(n-1)  +    L(n-2)   +  1                 [3^rd equation]  
                    ─── also ───
       L(n) =      2  *  Fib(n+1)   -  1                 [4^th equation]

where the + 1 will herein be known as the add number.

where the FIB is the Fibonacci numbers.

This task will be using the 3^rd equation (above) to calculate the Leonardo numbers.

Edsger W. Dijkstra used Leonardo numbers as an integral part of his smoothsort algorithm.

The first few Leonardo numbers are:

    1   1   3   5   9   15   25   41   67   109   177   287   465   753   1219   1973   3193   5167   8361  ···

Task

show the 1^st 25 Leonardo numbers, starting at L(0).
allow the first two Leonardo numbers to be specified [for L(0) and L(1)].
allow the add number to be specified (1 is the default).
show the 1^st 25 Leonardo numbers, specifying 0 and 1 for L(0) and L(1), and 0 for the add number.

(The last task requirement will produce the Fibonacci numbers.)

Show all output here on this page.

Related tasks

See also

11l

Translation of: C++

<lang 11l>F leo_numbers(cnt, =l0 = 1, =l1 = 1, add = 1)

  L 1..cnt
     print(l0, end' ‘ ’)
     (l0, l1) = (l1, l0 + l1 + add)
  print()

print(‘Leonardo Numbers: ’, end' ‘’) leo_numbers(25) print(‘Fibonacci Numbers: ’, end' ‘’) leo_numbers(25, 0, 1, 0)</lang>

Output:

Leonardo Numbers: 1 1 3 5 9 15 25 41 67 109 177 287 465 753 1219 1973 3193 5167 8361 13529 21891 35421 57313 92735 150049
Fibonacci Numbers: 0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765 10946 17711 28657 46368

Action!

<lang Action!>CARD FUNC Leonardo(BYTE n)

 CARD curr,prev,tmp

 IF n<=1 THEN
   RETURN (1)
 FI

 prev=1
 curr=1
 DO
   tmp=prev
   prev=curr
   curr==+tmp+1
   n==-1
 UNTIL n=1
 OD

RETURN (curr)

PROC Main()

 BYTE n
 CARD l

 Put(125) ;clear screen

 FOR n=0 TO 22 ;limited to 22 because of CARD limitations
 DO
   l=Leonardo(n)
   IF n MOD 2=0 THEN
     Position(2,n/2+1)
   ELSE
     Position(21,n/2+1)
   FI
   PrintF("L(%B)=%U",n,l)
 OD

RETURN</lang>

Output:

Screenshot from Atari 8-bit computer

L(0)=1             L(1)=1
L(2)=3             L(3)=5
L(4)=9             L(5)=15
L(6)=25            L(7)=41
L(8)=67            L(9)=109
L(10)=177          L(11)=287
L(12)=465          L(13)=753
L(14)=1219         L(15)=1973
L(16)=3193         L(17)=5167
L(18)=8361         L(19)=13529
L(20)=21891        L(21)=35421
L(22)=57313

Ada

<lang Ada>with Ada.Text_IO; use Ada.Text_IO;

procedure Leonardo is

  function Leo
    (N      : Natural;
     Step   : Natural := 1;
     First  : Natural := 1;
     Second : Natural := 1) return Natural   is 
     L : array (0..1) of Natural := (First, Second);

begin for i in 1 .. N loop L := (L(1), L(0)+L(1)+Step); end loop; return L (0); end Leo;

begin

  Put_Line ("First 25 Leonardo numbers:");
  for I in 0 .. 24 loop
     Put (Integer'Image (Leo (I)));
  end loop;
  New_Line;
  Put_Line ("First 25 Leonardo numbers with L(0) = 0, L(1) = 1, " &
            "step = 0 (fibonacci numbers):");
  for I in 0 .. 24 loop
     Put (Integer'Image (Leo (I, 0, 0, 1)));
  end loop;
  New_Line;

end Leonardo;</lang>

Output:

First 25 Leonardo numbers:
 1 1 3 5 9 15 25 41 67 109 177 287 465 753 1219 1973 3193 5167 8361 13529 21891 35421 57313 92735 150049
First 25 Leonardo numbers with L(0) = 0, L(1) = 1, step = 0 (fibonacci numbers):
 0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765 10946 17711 28657 46368

ALGOL 68

<lang algol68>BEGIN

   # leonardo number parameters #
   MODE LEONARDO = STRUCT( INT l0, l1, add number );
   # default leonardo number parameters #
   LEONARDO leonardo numbers = LEONARDO( 1, 1, 1 );
   # operators to allow us to specify non-default parameters #
   PRIO WITHLZERO = 9, WITHLONE = 9, WITHADDNUMBER = 9;
   OP   WITHLZERO     = ( LEONARDO parameters, INT l0         )LEONARDO:
        LEONARDO( l0, l1 OF parameters, add number OF parameters );
   OP   WITHLONE      = ( LEONARDO parameters, INT l1         )LEONARDO:
        LEONARDO( l0 OF parameters, l1, add number OF parameters );
   OP   WITHADDNUMBER = ( LEONARDO parameters, INT add number )LEONARDO:
        LEONARDO( l0 OF parameters, l1 OF parameters, add number );
   # show the first n Leonardo numbers with the specified parameters #
   PROC show = ( INT n, LEONARDO parameters )VOID:
        IF n > 0 THEN
           INT l0         = l0         OF parameters;
           INT l1         = l1         OF parameters;
           INT add number = add number OF parameters;
           print( ( whole( l0, 0 ), " " ) );
           IF n > 1 THEN
               print( ( whole( l1, 0 ), " " ) );
               INT lp := l0;
               INT ln := l1;
               FROM 2 TO n - 1 DO
                   INT next = ln + lp + add number;
                   lp := ln;
                   ln := next;
                   print( ( whole( ln, 0 ), " " ) )
               OD
           FI
        FI # show # ;

   # first series #
   print( ( "First 25 Leonardo numbers", newline ) );
   show( 25, leonardo numbers );
   print( ( newline ) );
   # second series #
   print( ( "First 25 Leonardo numbers from 0, 1 with add number = 0", newline ) );
   show( 25, leonardo numbers WITHLZERO 0 WITHADDNUMBER 0 );
   print( ( newline ) )

END</lang>

Output:

First 25 Leonardo numbers
1 1 3 5 9 15 25 41 67 109 177 287 465 753 1219 1973 3193 5167 8361 13529 21891 35421 57313 92735 150049
First 25 Leonardo numbers from 0, 1 with add number = 0
0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765 10946 17711 28657 46368

AppleScript

Functional

Translation of: Python

(Generator version)

Drawing N items from a non-finite generator: <lang applescript>------------------------ GENERATOR -------------------------

-- leo :: Int -> Int -> Int -> Generator [Int] on leo(L0, L1, delta)

   script
       property x : L0
       property y : L1
       on |λ|()
           set n to x
           set {x, y} to {y, x + y + delta}
           return n
       end |λ|
   end script

end leo

TEST ---------------------------

on run

   set leonardo to leo(1, 1, 1)
   set fibonacci to leo(0, 1, 0)
   
   unlines({"First 25 Leonardo numbers:", ¬
       twoLines(take(25, leonardo)), "", ¬
       "First 25 Fibonacci numbers:", ¬
       twoLines(take(25, fibonacci))})

end run

FORMATTING ------------------------

-- twoLines :: [Int] -> String on twoLines(xs)

   script row
       on |λ|(ns)
           tab & intercalate(", ", ns)
       end |λ|
   end script
   return unlines(map(row, chunksOf(16, xs)))

end twoLines

GENERIC --------------------------

-- chunksOf :: Int -> [a] -> a on chunksOf(n, xs)

   set lng to length of xs
   script go
       on |λ|(a, i)
           set x to (i + n) - 1
           if x ≥ lng then
               a & {items i thru -1 of xs}
           else
               a & {items i thru x of xs}
           end if
       end |λ|
   end script
   foldl(go, {}, enumFromThenTo(1, n, lng))

end chunksOf

-- enumFromThenTo :: Int -> Int -> Int -> [Int] on enumFromThenTo(x1, x2, y)

   set xs to {}
   set d to max(1, (x2 - x1))
   repeat with i from x1 to y by d
       set end of xs to i
   end repeat
   return xs

end enumFromThenTo

-- foldl :: (a -> b -> a) -> a -> [b] -> a on foldl(f, startValue, xs)

   tell mReturn(f)
       set v to startValue
       set lng to length of xs
       repeat with i from 1 to lng
           set v to |λ|(v, item i of xs, i, xs)
       end repeat
       return v
   end tell

end foldl

-- intercalate :: String -> [String] -> String on intercalate(sep, xs)

   set {dlm, my text item delimiters} to ¬
       {my text item delimiters, sep}
   set s to xs as text
   set my text item delimiters to dlm
   return s

end intercalate

-- Lift 2nd class handler function into 1st class script wrapper -- mReturn :: First-class m => (a -> b) -> m (a -> b) on mReturn(f)

   if class of f is script then
       f
   else
       script
           property |λ| : f
       end script
   end if

end mReturn

-- map :: (a -> b) -> [a] -> [b] on map(f, xs)

   tell mReturn(f)
       set lng to length of xs
       set lst to {}
       repeat with i from 1 to lng
           set end of lst to |λ|(item i of xs, i, xs)
       end repeat
       return lst
   end tell

end map

-- max :: Ord a => a -> a -> a on max(x, y)

   if x > y then
       x
   else
       y
   end if

end max

-- take :: Int -> [a] -> [a] -- take :: Int -> String -> String on take(n, xs)

   set c to class of xs
   if list is c then
       if 0 < n then
           items 1 thru min(n, length of xs) of xs
       else
           {}
       end if
   else if string is c then
       if 0 < n then
           text 1 thru min(n, length of xs) of xs
       else
           ""
       end if
   else if script is c then
       set ys to {}
       repeat with i from 1 to n
           set v to xs's |λ|()
           if missing value is v then
               return ys
           else
               set end of ys to v
           end if
       end repeat
       return ys
   else
       missing value
   end if

end take

-- unlines :: [String] -> String on unlines(xs)

   set {dlm, my text item delimiters} to ¬
       {my text item delimiters, linefeed}
   set str to xs as text
   set my text item delimiters to dlm
   str

end unlines</lang>

Output:

First 25 Leonardo numbers:
    1, 1, 3, 5, 9, 15, 25, 41, 67, 109, 177, 287, 465, 753, 1219, 1973
    1973, 3193, 5167, 8361, 13529, 21891, 35421, 57313, 92735, 150049

First 25 Fibonacci numbers:
    0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610
    610, 987, 1597, 2584, 4181, 6765, 10946, 17711, 28657, 46368

Idiomatic

Allowing optional 'L0', 'L1', and/or 'add' specs with any version of AppleScript. <lang applescript>-- spec: record containing none, some, or all of the 'L0', 'L1', and 'add' values. on leonardos(spec, quantity)

   -- Assign the spec values to variables, using defaults for any not given.
   set {L0:a, L1:b, add:inc} to spec & {L0:1, L1:1, add:1}
   -- Build the output list.
   script o
       property output : {a, b}
   end script
   repeat (quantity - 2) times
       set c to a + b + inc
       set end of o's output to c
       set a to b
       set b to c
   end repeat
   
   return o's output

end leonardos

local output, astid set astid to AppleScript's text item delimiters set AppleScript's text item delimiters to ", " set output to "1st 25 Leonardos: " & leonardos({}, 25) & " 1st 25 Fibonaccis: " & leonardos({L0:0, L1:1, add:0}, 25) set AppleScript's text item delimiters to astid return output</lang>

Output:

<lang applescript>"1st 25 Leonardos: 1, 1, 3, 5, 9, 15, 25, 41, 67, 109, 177, 287, 465, 753, 1219, 1973, 3193, 5167, 8361, 13529, 21891, 35421, 57313, 92735, 150049 1st 25 Fibonaccis: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946, 17711, 28657, 46368"</lang>

Arturo

<lang rebol>L: function [n l0 l1 ladd].memoize[

   (n=0)? -> l0 [
       (n=1)? -> l1
              -> (L n-1 l0 l1 ladd) + (L n-2 l0 l1 ladd) + ladd
   ]

]

Leonardo: function [z]-> L z 1 1 1

print "The first 25 Leonardo numbers:" print map 0..24 => Leonardo print "" print "The first 25 Leonardo numbers with L0=0, L1=1, LADD=0" print map 0..24 'x -> L x 0 1 0</lang>

Output:

The first 25 Leonardo numbers:
1 1 3 5 9 15 25 41 67 109 177 287 465 753 1219 1973 3193 5167 8361 13529 21891 35421 57313 92735 150049 

The first 25 Leonardo numbers with L0=0, L1=1, LADD=0
0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765 10946 17711 28657 46368

AutoHotkey

<lang AutoHotkey>Leonardo(n, L0:=1, L1:=1, step:=1){ if n=0 return L0 if n=1 return L1 return Leonardo(n-1, L0, L1, step) + Leonardo(n-2, L0, L1, step) + step }</lang> Examples:<lang AutoHotkey>output := "1st 25 Leonardo numbers, starting at L(0).`n" loop, 25 output .= Leonardo(A_Index-1) " " output .= "`n`n1st 25 Leonardo numbers, specifying 0 and 1 for L(0) and L(1), and 0 for the add number:`n" loop, 25 output .= Leonardo(A_Index-1, 0, 1, 0) " " MsgBox % output return</lang>

Output:

1st 25 Leonardo numbers, starting at L(0).
1 1 3 5 9 15 25 41 67 109 177 287 465 753 1219 1973 3193 5167 8361 13529 21891 35421 57313 92735 150049 

1st 25 Leonardo numbers, specifying 0 and 1 for L(0) and L(1), and 0 for the add number:
0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765 10946 17711 28657 46368

AWK

syntax: GAWK -f LEONARDO_NUMBERS.AWK

BEGIN {

   leonardo(1,1,1,"Leonardo")
   leonardo(0,1,0,"Fibonacci")
   exit(0)

} function leonardo(L0,L1,step,text, i,tmp) {

   printf("%s numbers (%d,%d,%d):\n",text,L0,L1,step)
   for (i=1; i<=25; i++) {
     if (i == 1) {
       printf("%d ",L0)
     }
     else if (i == 2) {
       printf("%d ",L1)
     }
     else {
       printf("%d ",L0+L1+step)
       tmp = L0
       L0 = L1
       L1 = tmp + L1 + step
     }
   }
   printf("\n")

} </lang>

Output:

Leonardo numbers (1,1,1):
1 1 3 5 9 15 25 41 67 109 177 287 465 753 1219 1973 3193 5167 8361 13529 21891 35421 57313 92735 150049
Fibonacci numbers (0,1,0):
0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765 10946 17711 28657 46368

Bash

!/bin/bash

function leonardo_number () {

   L0_value=${2:-1}
   L1_value=${3:-1}
   Add=${4:-1}
   leonardo_numbers=($L0_value $L1_value)
   for (( i = 2; i < $1; ++i))
   do
      leonardo_numbers+=( $((leonardo_numbers[i-1] + leonardo_numbers[i-2] + Add)) )
   done
   echo "${leonardo_numbers[*]}"

} </lang>

Output:

leonardo_number 25
1 1 3 5 9 15 25 41 67 109 177 287 465 753 1219 1973 3193 5167 8361 13529 21891 35421 57313 92735 150049

leonardo_number 25 0 1 0
0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765 10946 17711 28657 46368

BASIC

BASIC256

<lang BASIC256> subroutine leonardo(L0, L1, suma, texto) print "Numeros de " + texto + " (" + L0 + "," + L1 + "," + suma + "):" for i = 1 to 25 if i = 1 then print L0 + " "; else if i = 2 then print L1 + " "; else print L0 + L1 + suma + " "; tmp = L0 L0 = L1 L1 = tmp + L1 + suma end if end if next i print chr(10) end subroutine

--- Programa Principal ---

call leonardo(1,1,1,"Leonardo") call leonardo(0,1,0,"Fibonacci") end </lang>

Output:

Numeros de Leonardo (1,1,1):
1 1 3 5 9 15 25 41 67 109 177 287 465 753 1219 1973 3193 5167 8361 13529 21891 35421 57313 92735 150049 

Numeros de Fibonacci (0,1,0):
0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765 10946 17711 28657 46368

IS-BASIC

<lang IS-BASIC>100 PROGRAM "Leonardo.bas" 110 INPUT PROMPT "Enter values of L0, L1, and ADD, separated by comas: ":L0,L1,ADD 120 PRINT L0;L1; 130 FOR I=3 TO 25 140 LET T=L1:LET L1=L1+L0+ADD:LET L0=T 160 PRINT L1; 170 NEXT 180 PRINT</lang>

Sinclair ZX81 BASIC

Runs on the 1k RAM model with room to spare; hence the long(ish) variable names. The parameters are read from the keyboard. <lang basic> 10 INPUT L0

20 INPUT L1
30 INPUT ADD
40 PRINT L0;" ";L1;
50 FOR I=3 TO 25
60 LET TEMP=L1
70 LET L1=L0+L1+ADD
80 LET L0=TEMP
90 PRINT " ";L1;

100 NEXT I</lang>

Input:

1
1
1

Output:

1 1 3 5 9 15 25 41 67 109 177 287 465 753 1219 1973 3193 5167 8361 13529 21891 35421 57313 92735 150049

Input:

0
1
0

Output:

 0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765 10946 17711 28657 46368

BBC BASIC

It's a shame when fonts don't make much of a distinction between l lower-case L and 1 the number One. <lang bbcbasic>REM >leonardo

PRINT "Enter values of L0, L1, and ADD, separated by commas:" INPUT l0%, l1%, add% PRINT l0% ' l1% FOR i% = 3 TO 25

 temp% = l1%
 l1% += l0% + add%
 l0% = temp%
 PRINT l1%

NEXT PRINT END</lang>

Output:

Enter values of L0, L1, and ADD, separated by commas:
?1, 1, 1
         1
         1
         3
         5
         9
        15
        25
        41
        67
       109
       177
       287
       465
       753
      1219
      1973
      3193
      5167
      8361
     13529
     21891
     35421
     57313
     92735
    150049

Enter values of L0, L1, and ADD, separated by commas:
?0, 1, 0
         0
         1
         1
         2
         3
         5
         8
        13
        21
        34
        55
        89
       144
       233
       377
       610
       987
      1597
      2584
      4181
      6765
     10946
     17711
     28657
     46368

Burlesque

<lang burlesque>blsq ) 1 1 1{.+\/.+}\/+]23!CCLm]wdsh 1 1 3 5 9 15 25 41 67 109 177 287 465 753 1219 1973 3193 5167 8361 13529 21891 35421 57313 92735 150049

blsq ) 0 1 0{.+\/.+}\/+]23!CCLm]wdsh 0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765 10946 17711 28657 46368</lang>

C

This implementation fulfills the task requirements which state that the first 2 terms and the step increment should be specified. Many other implementations on this page only print out the first 25 numbers. <lang C>

include<stdio.h>

void leonardo(int a,int b,int step,int num){

int i,temp;

printf("First 25 Leonardo numbers : \n");

for(i=1;i<=num;i++){ if(i==1) printf(" %d",a); else if(i==2) printf(" %d",b); else{ printf(" %d",a+b+step); temp = a; a = b; b = temp+b+step; } } }

int main() { int a,b,step;

printf("Enter first two Leonardo numbers and increment step : ");

scanf("%d%d%d",&a,&b,&step);

leonardo(a,b,step,25);

return 0; } </lang> Output : Normal Leonardo Series :

Enter first two Leonardo numbers and increment step : 1 1 1
First 25 Leonardo numbers :
 1 1 3 5 9 15 25 41 67 109 177 287 465 753 1219 1973 3193 5167 8361 13529 21891 35421 57313 92735 150049

Fibonacci Series :

Enter first two Leonardo numbers and increment step : 0 1 0
First 25 Leonardo numbers :
 0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765 10946 17711 28657 46368

C#

Works with: C sharp version 7

<lang csharp>using System; using System.Linq;

public class Program {

   public static void Main() {
       Console.WriteLine(string.Join(" ", Leonardo().Take(25)));
       Console.WriteLine(string.Join(" ", Leonardo(L0: 0, L1: 1, add: 0).Take(25)));
   }

   public static IEnumerable<int> Leonardo(int L0 = 1, int L1 = 1, int add = 1) {
       while (true) {
           yield return L0;
           (L0, L1) = (L1, L0 + L1 + add);
       }
   }

}</lang>

Output:

1 1 3 5 9 15 25 41 67 109 177 287 465 753 1219 1973 3193 5167 8361 13529 21891 35421 57313 92735 150049
0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765 10946 17711 28657 46368

C++

include <iostream>

void leoN( int cnt, int l0 = 1, int l1 = 1, int add = 1 ) {

   int t;
   for( int i = 0; i < cnt; i++ ) {
       std::cout << l0 << " ";
       t = l0 + l1 + add; l0 = l1; l1 = t;
   }

} int main( int argc, char* argv[] ) {

   std::cout << "Leonardo Numbers: "; leoN( 25 );
   std::cout << "\n\nFibonacci Numbers: "; leoN( 25, 0, 1, 0 );
   return 0;

} </lang>

Output:

Leonardo Numbers: 1 1 3 5 9 15 25 41 67 109 177 287 465 753 1219 1973 3193 5167 8361 13529 21891 35421 57313 92735 150049

Fibonacci Numbers: 0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765 10946 17711 28657 46368

Common Lisp

leo - calculates the first n number from a leo sequence. The first argument n is the number of values to return. The next three arguments a, b, add are optional. Default values provide the "original" leonardo numbers as defined in the task. a and b are the first and second element of the leonardo sequence. add is the "add number" as defined in the task definition.

(defun leo (n &optional (a 1) (b 1) (add 1))

 (labels ((iterate (n foo)
            (if (zerop n) (reverse foo)
                          (iterate (- n 1)
                                   (cons (+ (first foo) (second foo) add) foo)))))
    (cond ((= n 1) (list a))
          (T       (iterate (- n 2) (list b a))))))

</lang>

Output:

> (leo 25)
(1 1 3 5 9 15 25 41 67 109 177 287 465 753 1219 1973 3193 5167 8361 13529 21891 35421 57313 92735 150049)
> (leo 25 0 1 0)
(0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765 10946 17711 28657 46368)

Crystal

Translation of: Python

<lang ruby>def leonardo(l_zero, l_one, add, amount)

   terms = [l_zero, l_one]
   while terms.size < amount
       new = terms[-1] + terms[-2]
       new += add
       terms << new
   end
   terms

end

puts "First 25 Leonardo numbers: \n#{ leonardo(1,1,1,25) }" puts "Leonardo numbers with fibonacci parameters:\n#{ leonardo(0,1,0,25) }" </lang>

Output:

First 25 Leonardo numbers: 
[1, 1, 3, 5, 9, 15, 25, 41, 67, 109, 177, 287, 465, 753, 1219, 1973, 3193, 5167, 8361, 13529, 21891, 35421, 57313, 92735, 150049]
Leonardo numbers with fibonacci parameters:
[0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946, 17711, 28657, 46368]

D

Translation of: C++

<lang D> import std.stdio;

void main() {

   write("Leonardo Numbers: ");
   leonardoNumbers( 25 );

   write("Fibonacci Numbers: ");
   leonardoNumbers( 25, 0, 1, 0 );

}

void leonardoNumbers(int count, int l0=1, int l1=1, int add=1) {

   int t;
   for (int i=0; i<count; ++i) {
       write(l0, " ");
       t = l0 + l1 + add;
       l0 = l1;
       l1 = t;
   }
   writeln();

} </lang>

Output:

Leonardo Numbers: 1 1 3 5 9 15 25 41 67 109 177 287 465 753 1219 1973 3193 5167 8361 13529 21891 35421 57313 92735 150049 Fibonacci Numbers: 0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765 10946 17711 28657 46368

F#

Translation of: Haskell

<lang fsharp>open System

let leo l0 l1 d =

   Seq.unfold (fun (x, y) -> Some (x, (y, x + y + d))) (l0, l1)

let leonardo = leo 1 1 1 let fibonacci = leo 0 1 0

[<EntryPoint>] let main _ =

   let leoNums = Seq.take 25 leonardo |> Seq.chunkBySize 16
   printfn "First 25 of the (1, 1, 1) Leonardo numbers:\n%A" leoNums
   Console.WriteLine()

   let fibNums = Seq.take 25 fibonacci |> Seq.chunkBySize 16
   printfn "First 25 of the (0, 1, 0) Leonardo numbers (= Fibonacci number):\n%A" fibNums

   0 // return an integer exit code</lang>

Output:

First 25 of the (1, 1, 1) Leonardo numbers:
seq
  [[|1; 1; 3; 5; 9; 15; 25; 41; 67; 109; 177; 287; 465; 753; 1219; 1973|];
   [|3193; 5167; 8361; 13529; 21891; 35421; 57313; 92735; 150049|]]

First 25 of the (0, 1, 0) Leonardo numbers (= Fibonacci number):
seq
  [[|0; 1; 1; 2; 3; 5; 8; 13; 21; 34; 55; 89; 144; 233; 377; 610|];
   [|987; 1597; 2584; 4181; 6765; 10946; 17711; 28657; 46368|]]

Factor

<lang>USING: fry io kernel math prettyprint sequences ; IN: rosetta-code.leonardo-numbers

first25-leonardo ( vector add -- seq )

   23 swap '[ dup 2 tail* sum _ + over push ] times ;

print-leo ( seq -- ) [ pprint bl ] each nl ;

"First 25 Leonardo numbers:" print V{ 1 1 } 1 first25-leonardo print-leo

"First 25 Leonardo numbers with L(0)=0, L(1)=1, add=0:" print V{ 0 1 } 0 first25-leonardo print-leo</lang>

Output:

First 25 Leonardo numbers:
1 1 3 5 9 15 25 41 67 109 177 287 465 753 1219 1973 3193 5167 8361 13529 21891 35421 57313 92735 150049
First 25 Leonardo numbers with L(0)=0, L(1)=1, add=0:
0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765 10946 17711 28657 46368

Fermat

<lang fermat>Func Leonardo(size, l0, l1, add) =

   Array leo[1,size];             {set up as a row rather than column vector; looks nicer to print}
   leo[1,1]:=l0; leo[1,2]:=l1;    {fermat arrays are 1-indexed}
   for i=3 to size do
       leo[1,i]:=leo[1,i-2]+leo[1,i-1]+add;
   od;
   .;

Leonardo(25, 1, 1, 1); [leo];

Leonardo(25, 0, 1, 0); [leo];</lang>

Output:

[[  1,  1,  3,  5,  9,  15, 25, 41, 67, 109, 177, 287, 465, 753, 1219, 1973, 3193, 5167, 8361, 13529, 21891, 35421, 57313, 92735, 150049  ]]

[[[  1,  1,  3,  5,  9,  15, 25, 41, 67, 109, 177, 287, 465, 753, 1219, 1973, 3193, 5167, 8361, 13529, 21891, 35421, 57313, 92735, 150049  ]]

Fortran

Happily, no monster values result for the trial run, so ordinary 32-bit integers suffice. The source style uses the F90 facilities only to name the subroutine being ended (i.e. END SUBROUTINE LEONARDO rather than just END) and the I0 format code that shows an integer without a fixed space allowance, convenient in produced well-formed messages. The "$" format code signifies that the end of output from its WRITE statement should not trigger the starting of a new line for the next WRITE statement, convenient when rolling a sequence of values to a line of output one-by-one as they are concocted. Otherwise, the values would have to be accumulated in a suitable array and then written in one go.

Many versions of Fortran have enabled parameters to be optionally supplied and F90 has standardised a protocol, also introducing a declaration syntax that can specify multiple attributes in one statement which in this case would be INTEGER, OPTIONAL:: AF rather than two statements concerning AF. However, in a test run with CALL LEONARDO(25,1,1) the Compaq F90/95 compiler rejected this attempt because there was another invocation with four parameters, not three, in the same program unit. By adding the rigmarole for declaring a MODULE containing the subroutine LEONARDO, its worries would be assuaged. Many compilers (and linkers, for separately-compiled routines) would check neither the number nor the type of parameters so no such complaint would be made - but when run, the code might produce wrong results or crash.

The method relies on producing a sequence of values, rather than calculating L(n) from the start each time a value from the sequence is required. <lang Fortran> SUBROUTINE LEONARDO(LAST,L0,L1,AF) !Show the first LAST values of the sequence.

      INTEGER LAST	!Limit to show.
      INTEGER L0,L1	!Starting values.
      INTEGER AF	!The "Add factor" to deviate from Fibonacci numbers.
      OPTIONAL AF	!Indicate that this parameter may be omitted.
      INTEGER EMBOLISM	!The bloat to employ.
      INTEGER N,LN,LNL1,LNL2	!Assistants to the calculation.
       IF (PRESENT(AF)) THEN	!Perhaps the last parameter has not been given.
         EMBOLISM = AF			!It has. Take its value.
        ELSE			!But if not,
         EMBOLISM = 1			!This is the specified default.
       END IF			!Perhaps there should be some report on this?
       WRITE (6,1) LAST,L0,L1,EMBOLISM	!Announce.
   1   FORMAT ("The first ",I0,	!The I0 format code avoids excessive spacing.
    1   " numbers in the Leonardo sequence defined by L(0) = ",I0,
    2   " and L(1) = ",I0," with L(n) = L(n - 1) + L(n - 2) + ",I0)
       IF (LAST .GE. 1) WRITE (6,2) L0	!In principle, LAST may be small.
       IF (LAST .GE. 2) WRITE (6,2) L1	!!So, suspicion rules.
   2   FORMAT (I0,", ",$)	!Obviously, the $ sez "don't finish the line".
       LNL1 = L0	!Syncopation for the sequence's initial values.
       LN = L1		!Since the parameters ought not be damaged.
       DO N = 3,LAST	!Step away.
         LNL2 = LNL1		!Advance the two state variables one step.
         LNL1 = LN		!Ready to make a step forward.
         LN = LNL1 + LNL2 + EMBOLISM	!Thus.
         WRITE (6,2) LN	!Reveal the value. Overflow is distant...
       END DO		!On to the next step.
       WRITE (6,*)	!Finish the line.
     END SUBROUTINE LEONARDO	!Only speedy for the sequential production of values.

     PROGRAM POKE

     CALL LEONARDO(25,1,1,1)	!The first 25 Leonardo numbers.
     CALL LEONARDO(25,0,1,0)	!Deviates to give the Fibonacci sequence.
     END </lang>

Output:

The first 25 numbers in the Leonardo sequence defined by L(0) = 1 and L(1) = 1 with L(n) = L(n - 1) + L(n - 2) + 1
1, 1, 3, 5, 9, 15, 25, 41, 67, 109, 177, 287, 465, 753, 1219, 1973, 3193, 5167, 8361, 13529, 21891, 35421, 57313, 92735, 150049,
The first 25 numbers in the Leonardo sequence defined by L(0) = 0 and L(1) = 1 with L(n) = L(n - 1) + L(n - 2) + 0
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946, 17711, 28657, 46368,

FreeBASIC

<lang freebasic> Sub leonardo(L0 As Integer, L1 As Integer, suma As Integer, texto As String)

   Dim As Integer i, tmp
   Print "Numeros de " &texto &" (" &L0 &"," &L1 &"," &suma &"):"
   For i = 1 To 25
       If i = 1 Then
           Print L0;
       Elseif i = 2 Then
           Print L1;
       Else
           Print L0 + L1 + suma;
           tmp = L0
           L0 = L1
           L1 = tmp + L1 + suma
       End If
   Next i
   Print Chr(10)

End Sub

'--- Programa Principal --- leonardo(1,1,1,"Leonardo") leonardo(0,1,0,"Fibonacci") End </lang>

Output:

Numeros de Leonardo (1,1,1):
 1 1 3 5 9 15 25 41 67 109 177 287 465 753 1219 1973 3193 5167 8361 13529 21891 35421 57313 92735 150049

Numeros de Fibonacci (0,1,0):
 0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765 10946 17711 28657 46368

Go

<lang go>package main

import "fmt"

func leonardo(n, l0, l1, add int) []int {

   leo := make([]int, n)
   leo[0] = l0
   leo[1] = l1
   for i := 2; i < n; i++ {
       leo[i] = leo[i - 1] + leo[i - 2] + add
   }
   return leo

}

func main() {

   fmt.Println("The first 25 Leonardo numbers with L[0] = 1, L[1] = 1 and add number = 1 are:")
   fmt.Println(leonardo(25, 1, 1, 1))
   fmt.Println("\nThe first 25 Leonardo numbers with L[0] = 0, L[1] = 1 and add number = 0 are:")
   fmt.Println(leonardo(25, 0, 1, 0))

}</lang>

Output:

The first 25 Leonardo numbers with L[0] = 1, L[1] = 1 and add number = 1 are:
[1 1 3 5 9 15 25 41 67 109 177 287 465 753 1219 1973 3193 5167 8361 13529 21891 35421 57313 92735 150049]

The first 25 Leonardo numbers with L[0] = 0, L[1] = 1 and add number = 0 are:
[0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765 10946 17711 28657 46368]

Haskell

<lang Haskell>import Data.List (intercalate, unfoldr) import Data.List.Split (chunksOf)

LEONARDO NUMBERS ---------------------

-- L0 -> L1 -> Add number -> Series (infinite) leo :: Integer -> Integer -> Integer -> [Integer] leo l0 l1 d = unfoldr (\(x, y) -> Just (x, (y, x + y + d))) (l0, l1)

leonardo :: [Integer] leonardo = leo 1 1 1

fibonacci :: [Integer] fibonacci = leo 0 1 0

TEST ---------------------------

main :: IO () main =

 (putStrLn . unlines)
   [ "First 25 default (1, 1, 1) Leonardo numbers:\n"
   , f $ take 25 leonardo
   , "First 25 of the (0, 1, 0) Leonardo numbers (= Fibonacci numbers):\n"
   , f $ take 25 fibonacci
   ]
 where
   f = unlines . fmap (('\t' :) . intercalate ",") . chunksOf 16 . fmap show</lang>

Output:

First 25 default (1, 1, 1) Leonardo numbers:

    1,1,3,5,9,15,25,41,67,109,177,287,465,753,1219,1973
    3193,5167,8361,13529,21891,35421,57313,92735,150049

First 25 of the (0, 1, 0) Leonardo numbers (= Fibonacci numbers):

    0,1,1,2,3,5,8,13,21,34,55,89,144,233,377,610
    987,1597,2584,4181,6765,10946,17711,28657,46368

Alternately, defining the list self-referentially instead of using unfoldr: <lang haskell>leo :: Integer -> Integer -> Integer -> [Integer] leo l0 l1 d = s where

 s = l0 : l1 : zipWith (\x y -> x + y + d) s (tail s)</lang>

J

Output:

 1 25 leo 1 1
1 1 3 5 9 15 25 41 67 109 177 287 465 753 1219 1973 3193 5167 8361 13529 21891 35421 57313 92735 150049

 0 25 leo 0 1
0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765 10946 17711 28657 46368

Java

Translation of: Kotlin

<lang Java>import java.util.Arrays; import java.util.List;

@SuppressWarnings("SameParameterValue") public class LeonardoNumbers {

   private static List<Integer> leonardo(int n) {
       return leonardo(n, 1, 1, 1);
   }

   private static List<Integer> leonardo(int n, int l0, int l1, int add) {
       Integer[] leo = new Integer[n];
       leo[0] = l0;
       leo[1] = l1;
       for (int i = 2; i < n; i++) {
           leo[i] = leo[i - 1] + leo[i - 2] + add;
       }
       return Arrays.asList(leo);
   }

   public static void main(String[] args) {
       System.out.println("The first 25 Leonardo numbers with L[0] = 1, L[1] = 1 and add number = 1 are:");
       System.out.println(leonardo(25));
       System.out.println("\nThe first 25 Leonardo numbers with L[0] = 0, L[1] = 1 and add number = 0 are:");
       System.out.println(leonardo(25, 0, 1, 0));
   }

}</lang>

Output:

The first 25 Leonardo numbers with L[0] = 1, L[1] = 1 and add number = 1 are:
[1, 1, 3, 5, 9, 15, 25, 41, 67, 109, 177, 287, 465, 753, 1219, 1973, 3193, 5167, 8361, 13529, 21891, 35421, 57313, 92735, 150049]

The first 25 Leonardo numbers with L[0] = 0, L[1] = 1 and add number = 0 are:
[0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946, 17711, 28657, 46368]

JavaScript

ES6

<lang JavaScript>const leoNum = (c, l0 = 1, l1 = 1, add = 1) =>

   new Array(c).fill(add).reduce(
       (p, c, i) => i > 1 ? (
           p.push(p[i - 1] + p[i - 2] + c) && p
       ) : p, [l0, l1]
   );

console.log(leoNum(25)); console.log(leoNum(25, 0, 1, 0));</lang>

[1, 1, 3, 5, 9, 15, 25, 41, 67, 109, 177, 287, 465, 753, 1219, 1973, 3193, 5167, 8361, 13529, 21891, 35421, 57313, 92735, 150049]
[0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946, 17711, 28657, 46368]

Or, taking N terms from a non-finite Javascript generator:

Translation of: Python

<lang javascript>(() => {

   'use strict';

   // leo :: Int -> Int -> Int -> Generator [Int]
   function* leo(L0, L1, delta) {
       let [x, y] = [L0, L1];
       while (true) {
           yield x;
           [x, y] = [y, delta + x + y];
       }
   }

   // ----------------------- TEST ------------------------
   // main :: IO ()
   const main = () => {
       const
           leonardo = leo(1, 1, 1),
           fibonacci = leo(0, 1, 0);

       return unlines([
           'First 25 Leonardo numbers:',
           indentWrapped(take(25)(leonardo)),
           ,
           'First 25 Fibonacci numbers:',
           indentWrapped(take(25)(fibonacci))
       ]);
   };

   // -------------------- FORMATTING ---------------------

   // indentWrapped :: [Int] -> String
   const indentWrapped = xs =>
       unlines(
           map(x => '\t' + x.join(','))(
               chunksOf(16)(
                   map(str)(xs)
               )
           )
       );

   // ----------------- GENERIC FUNCTIONS -----------------

   // chunksOf :: Int -> [a] -> a
   const chunksOf = n =>
       xs => enumFromThenTo(0)(n)(
           xs.length - 1
       ).reduce(
           (a, i) => a.concat([xs.slice(i, (n + i))]),
           []
       );

   // enumFromThenTo :: Int -> Int -> Int -> [Int]
   const enumFromThenTo = x1 =>
       x2 => y => {
           const d = x2 - x1;
           return Array.from({
               length: Math.floor(y - x2) / d + 2
           }, (_, i) => x1 + (d * i));
       };

   // map :: (a -> b) -> [a] -> [b]
   const map = f =>
       // The list obtained by applying f
       // to each element of xs.
       // (The image of xs under f).
       xs => [...xs].map(f);

   // str :: a -> String
   const str = x =>
       x.toString();

   // take :: Int -> [a] -> [a]
   // take :: Int -> String -> String
   const take = n =>
       // The first n elements of a list,
       // string of characters, or stream.
       xs => 'GeneratorFunction' !== xs
       .constructor.constructor.name ? (
           xs.slice(0, n)
       ) : [].concat.apply([], Array.from({
           length: n
       }, () => {
           const x = xs.next();
           return x.done ? [] : [x.value];
       }));

   // unlines :: [String] -> String
   const unlines = xs => xs.join('\n');

   // MAIN ---
   return main();

})();</lang>

Output:

First 25 Leonardo numbers:
    1,1,3,5,9,15,25,41,67,109,177,287,465,753,1219,1973
    3193,5167,8361,13529,21891,35421,57313,92735,150049

First 25 Fibonacci numbers:
    0,1,1,2,3,5,8,13,21,34,55,89,144,233,377,610
    987,1597,2584,4181,6765,10946,17711,28657,46368

jq

Naive Implementation

<lang jq>def Leonardo(zero; one; incr):

 def leo:
   if . == 0 then zero
   elif . == 1 then one
   else ((.-1) |leo) + ((.-2) | leo) +  incr
   end;
 leo;</lang>

Implementation with Caching

An array is used for caching, with `.[n]` storing the value L(n). <lang jq>def Leonardo(zero; one; incr):

 def leo(n):
   if .[n] then .
   else leo(n-1)   # optimization of leo(n-2)|leo(n-1)  
   | .[n] = .[n-1] + .[n-2] +  incr
   end;
 . as $n | [zero,one] | leo($n) | .[$n];</lang>

(To compute the sequence of Leonardo numbers L(1) ... L(n) without redundant computation, the last element of the pipeline in the last line of the function above should be dropped.)

Examples

<lang jq>[range(0;25) | Leonardo(1;1;1)]</lang>

Output:

[1,1,3,5,9,15,25,41,67,109,177,287,465,753,1219,1973,3193,5167,8361,13529,21891,35421,57313,92735,150049]

<lang jq>[range(0;25) | Leonardo(0;1;0)]</lang>

Output:

[0,1,1,2,3,5,8,13,21,34,55,89,144,233,377,610,987,1597,2584,4181,6765,10946,17711,28657,46368]

Julia

Works with: Julia version 0.6

<lang julia>function L(n, add::Int=1, firsts::Vector=[1, 1])

   l = max(maximum(n) .+ 1, length(firsts))
   r = Vector{Int}(l)
   r[1:length(firsts)] = firsts
   for i in 3:l
       r[i] = r[i - 1] + r[i - 2] + add
   end
   return r[n .+ 1]

end

Task 1

println("First 25 Leonardo numbers: ", join(L(0:24), ", "))

Task 2

@show L(0) L(1)

Task 4

println("First 25 Leonardo numbers starting with [0, 1]: ", join(L(0:24, 0, [0, 1]), ", "))</lang>

Output:

First 25 Leonardo numbers: 1, 1, 3, 5, 9, 15, 25, 41, 67, 109, 177, 287, 465, 753, 1219, 1973, 3193, 5167, 8361, 13529, 21891, 35421, 57313, 92735, 150049
L(0) = 1
L(1) = 1
First 25 Leonardo numbers starting with 0, 1: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946, 17711, 28657, 46368

Kotlin

<lang scala>// version 1.1.2

fun leonardo(n: Int, l0: Int = 1, l1: Int = 1, add: Int = 1): IntArray {

   val leo = IntArray(n)
   leo[0] = l0
   leo[1] = l1
   for (i in 2 until n) leo[i] = leo[i - 1] + leo[i - 2] + add
   return leo

}

fun main(args: Array<String>) {

   println("The first 25 Leonardo numbers with L[0] = 1, L[1] = 1 and add number = 1 are:")
   println(leonardo(25).joinToString(" "))
   println("\nThe first 25 Leonardo numbers with L[0] = 0, L[1] = 1 and add number = 0 are:")
   println(leonardo(25, 0, 1, 0).joinToString(" "))

}</lang>

Output:

The first 25 Leonardo numbers with L[0] = 1, L[1] = 1 and add number = 1 are:
1 1 3 5 9 15 25 41 67 109 177 287 465 753 1219 1973 3193 5167 8361 13529 21891 35421 57313 92735 150049

The first 25 Leonardo numbers with L[0] = 0, L[1] = 1 and add number = 0 are:
0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765 10946 17711 28657 46368

Lua

<lang lua>function leoNums (n, L0, L1, add)

 local L0, L1, add = L0 or 1, L1 or 1, add or 1
 local lNums, nextNum = {L0, L1}
 while #lNums < n do
   nextNum = lNums[#lNums] + lNums[#lNums - 1] + add
   table.insert(lNums, nextNum)
 end
 return lNums

end

function show (msg, t)

 print(msg .. ":")
 for i, x in ipairs(t) do
   io.write(x .. " ")
 end
 print("\n")

end

show("Leonardo numbers", leoNums(25)) show("Fibonacci numbers", leoNums(25, 0, 1, 0))</lang>

Output:

Leonardo numbers:
1 1 3 5 9 15 25 41 67 109 177 287 465 753 1219 1973 3193 5167 8361 13529 21891 35421 57313 92735 150049

Fibonacci numbers:
0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765 10946 17711 28657 46368

Maple

<lang Maple>L := proc(n, L_0, L_1, add) if n = 0 then

 return L_0;

elif n = 1 then

 return L_1;

else

 return L(n - 1) + L(n - 2) + add;

end if; end proc:

Leonardo := n -> (L(1, 1, 1),[seq(0..n - 1)])

Fibonacci := n -> (L(0, 1, 0), [seq(0..n - 1)])</lang>

[1, 1, 3, 5, 9, 15, 25, 41, 67, 109, 177, 287, 465, 753, 1219, 1973, 3193, 5167, 8361, 13529, 21891, 35421, 57313, 92735, 150049]
[0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946, 17711, 28657, 46368]

Mathematica/Wolfram Language

<lang Mathematica>L[0,L0_:1,___]:=L0 L[1,L0_:1,L1_:1,___]:=L1 L[n_,L0_:1,L1_:1,add_:1]:=L[n-1,L0,L1,add]+L[n-2,L0,L1,add]+add

L/@(Range[25]-1) L[#,0,1,0]&/@(Range[25]-1)</lang>

{1, 1, 3, 5, 9, 15, 25, 41, 67, 109, 177, 287, 465, 753, 1219, 1973, 3193, 5167, 8361, 13529, 21891, 35421, 57313, 92735, 150049}
{0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946, 17711, 28657, 46368}

min

Works with: min version 0.19.3

<lang min>(over over + rolldown pop pick +) :next (('print dip " " print! next) 25 times newline) :leo

"First 25 Leonardo numbers:" puts! 1 1 1 leo "First 25 Leonardo numbers with add=0, L(0)=0, L(1)=1:" puts! 0 0 1 leo</lang>

Output:

First 25 Leonardo numbers:
1 1 3 5 9 15 25 41 67 109 177 287 465 753 1219 1973 3193 5167 8361 13529 21891 35421 57313 92735 150049
First 25 Leonardo numbers with add=0, L(0)=0, L(1)=1:
0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765 10946 17711 28657 46368

Modula-2

<lang modula2>MODULE Leonardo; FROM FormatString IMPORT FormatString; FROM Terminal IMPORT WriteString,WriteLn,ReadChar;

PROCEDURE leonardo(a,b,step,num : INTEGER); VAR

   buf : ARRAY[0..63] OF CHAR;
   i,temp : INTEGER;

BEGIN

   FOR i:=1 TO num DO
       IF i=1 THEN
           FormatString(" %i", buf, a);
           WriteString(buf)
       ELSIF i=2 THEN
           FormatString(" %i", buf, b);
           WriteString(buf)
       ELSE
           FormatString(" %i", buf, a+b+step);
           WriteString(buf);

           temp := a;
           a := b;
           b := temp + b + step
       END
   END;
   WriteLn

END leonardo;

BEGIN

   leonardo(1,1,1,25);
   leonardo(0,1,0,25);

   ReadChar

END Leonardo.</lang>

Nim

<lang Nim>import strformat

proc leonardoNumbers(count: int, L0: int = 1,

                    L1: int = 1, ADD: int = 1) =
 var t = 0
 var (L0_loc, L1_loc) = (L0, L1)
 for i in 0..<count:
   write(stdout, fmt"{L0_loc:7}")
   t = L0_loc + L1_loc + ADD
   L0_loc = L1_loc
   L1_loc = t
   if i mod 5 == 4:
     write(stdout, "\n")
 write(stdout, "\n")

echo "Leonardo Numbers:" leonardoNumbers(25) echo "Fibonacci Numbers: " leonardoNumbers(25, 0, 1, 0)</lang>

Output:

Leonardo Numbers:
      1      1      3      5      9
     15     25     41     67    109
    177    287    465    753   1219
   1973   3193   5167   8361  13529
  21891  35421  57313  92735 150049

Fibonacci Numbers: 
      0      1      1      2      3
      5      8     13     21     34
     55     89    144    233    377
    610    987   1597   2584   4181
   6765  10946  17711  28657  46368

Perl

<lang perl>no warnings 'experimental::signatures'; use feature 'signatures';

sub leonardo ($n, $l0 = 1, $l1 = 1, $add = 1) {

 ($l0, $l1) = ($l1, $l0+$l1+$add)  for 1..$n;
 $l0;

}

my @L = map { leonardo($_) } 0..24; print "Leonardo[1,1,1]: @L\n"; my @F = map { leonardo($_,0,1,0) } 0..24; print "Leonardo[0,1,0]: @F\n";</lang>

Output:

Leonardo[1,1,1]: 1 1 3 5 9 15 25 41 67 109 177 287 465 753 1219 1973 3193 5167 8361 13529 21891 35421 57313 92735 150049
Leonardo[0,1,0]: 0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765 10946 17711 28657 46368

Phix

with javascript_semantics
function leonardo(integer n, l1=1, l2=1, step=1)
-- return the first n leonardo numbers, starting {l1,l2}, with step as the add number
    sequence res = {l1,l2}
    while length(res)<n do
        res = append(res,res[$]+res[$-1]+step)
    end while
    return res
end function
?{"Leonardo",leonardo(25)}
?{"Fibonacci",leonardo(25,0,1,0)}

Output:

{"Leonardo",{1,1,3,5,9,15,25,41,67,109,177,287,465,753,1219,1973,3193,5167,8361,13529,21891,35421,57313,92735,150049}}
{"Fibonacci",{0,1,1,2,3,5,8,13,21,34,55,89,144,233,377,610,987,1597,2584,4181,6765,10946,17711,28657,46368}}

PicoLisp

<lang PicoLisp>(de leo (A B C)

  (default A 1  B 1  C 1)
  (make
     (do 25
        (inc
           'B
           (+ (link (swap 'A B)) C) ) ) ) )

(println 'Leonardo (leo)) (println 'Fibonacci (leo 0 1 0))</lang>

Output:

Leonardo (1 1 3 5 9 15 25 41 67 109 177 287 465 753 1219 1973 3193 5167 8361 13529 21891 35421 57313 92735 150049)
Fibonacci (0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765 10946 17711 28657 46368)

Plain English

<lang plainenglish>To run: Start up. Write "First 25 Leonardo numbers:" on the console. Show 25 of the Leonardo numbers starting with 1 and 1 and using 1 for the add number. Write "First 25 Leonardo numbers with L(0)=0, L(1)=1, add=0:" on the console. Show 25 of the Leonardo numbers starting with 0 and 1 and using 0 for the add number. Wait for the escape key. Shut down.

To show a number of the Leonardo numbers starting with a first number and a second number and using an add number for the add number: If the number is less than 2, exit. Privatize the number. Privatize the first number. Privatize the second number. Subtract 2 from the number. Write the first number then " " then the second number on the console without advancing. Loop. If a counter is past the number, write "" on the console; exit. Swap the first number with the second number. Put the first number plus the second number plus the add number into the second number. Write the second number then " " on the console without advancing. Repeat.</lang>

Output:

First 25 Leonardo numbers:
1 1 3 5 9 15 25 41 67 109 177 287 465 753 1219 1973 3193 5167 8361 13529 21891 35421 57313 92735 150049
First 25 Leonardo numbers with L(0)=0, L(1)=1, add=0:
0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765 10946 17711 28657 46368

PureBasic

<lang purebasic> EnableExplicit

N = 25

Procedure leon_R(a.i, b.i, s.i = 1, n.i = #N)

 If n>2
   Print(Space(1) + Str(a + b + s))    
   ProcedureReturn leon_R(b, a + b + s, s, n-1)
 EndIf

EndProcedure

If OpenConsole()

 Define r$
 
 Print("Enter first two Leonardo numbers and increment step (separated by space) : ")
 r$ = Input()
 PrintN("First " + Str(#N) + " Leonardo numbers : ")  
 Print(StringField(r$, 1, Chr(32)) + Space(1) + 
       StringField(r$, 2, Chr(32)))
 
 leon_R(Val(StringField(r$, 1, Chr(32))),
        Val(StringField(r$, 2, Chr(32))),           
        Val(StringField(r$, 3, Chr(32))))
 
 r$ = Input()

EndIf </lang>

Output:

Enter first two Leonardo numbers and increment step (separated by space) : 1 1 1
First 25 Leonardo numbers :
1 1 3 5 9 15 25 41 67 109 177 287 465 753 1219 1973 3193 5167 8361 13529 21891 35421 57313 92735 150049
Enter first two Leonardo numbers and increment step (separated by space) : 0 1 0
First 25 Leonardo numbers :
0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765 10946 17711 28657 46368

Python

Finite iteration

<lang python>def Leonardo(L_Zero, L_One, Add, Amount):

   terms = [L_Zero,L_One]
   while len(terms) < Amount:
       new = terms[-1] + terms[-2]
       new += Add
       terms.append(new)
   return terms

out = "" print "First 25 Leonardo numbers:" for term in Leonardo(1,1,1,25):

   out += str(term) + " "

print out

out = "" print "Leonardo numbers with fibonacci parameters:" for term in Leonardo(0,1,0,25):

   out += str(term) + " "

print out </lang>

Output:

First 25 Leonardo numbers:
1 1 3 5 9 15 25 41 67 109 177 287 465 753 1219 1973 3193 5167 8361 13529 21891 35421 57313 92735 150049 
Leonardo numbers with fibonacci parameters:
0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765 10946 17711 28657 46368

Non-finite generation

Or, for a non-finite stream of Leonardos, we can use a Python generator:

Works with: Python version 3

<lang python>Leonardo numbers

from functools import (reduce) from itertools import (islice)

leo :: Int -> Int -> Int -> Generator [Int]

def leo(L0, L1, delta):

   A number series of the
      Leonardo and Fibonacci pattern,
      where L0 and L1 are the first two terms,
      and delta = 1 for (L0, L1) == (1, 1)
      yields the Leonardo series, while
      delta = 0 defines the Fibonacci series.
   (x, y) = (L0, L1)
   while True:
       yield x
       (x, y) = (y, x + y + delta)

main :: IO()

def main():

   Tests.

   print('\n'.join([
       'First 25 Leonardo numbers:',
       folded(16)(take(25)(
           leo(1, 1, 1)
       )),
       ,
       'First 25 Fibonacci numbers:',
       folded(16)(take(25)(
           leo(0, 1, 0)
       ))
   ]))

FORMATTING ----------------------------------------------

folded :: Int -> [a] -> String

def folded(n):

   Long list folded to rows of n terms each.
   return lambda xs: '[' + ('\n '.join(
       str(ns)[1:-1] for ns in chunksOf(n)(xs)
   ) + ']')

GENERIC -------------------------------------------------

chunksOf :: Int -> [a] -> a

def chunksOf(n):

   A series of lists of length n,
      subdividing the contents of xs.
      Where the length of xs is not evenly divible,
      the final list will be shorter than n.
   return lambda xs: reduce(
       lambda a, i: a + [xs[i:n + i]],
       range(0, len(xs), n), []
   ) if 0 < n else []

take :: Int -> [a] -> [a]
take :: Int -> String -> String

def take(n):

   The prefix of xs of length n,
      or xs itself if n > length xs.
   return lambda xs: (
       xs[0:n]
       if isinstance(xs, list)
       else list(islice(xs, n))
   )

MAIN ---

if __name__ == '__main__':

   main()</lang>

Output:

First 25 Leonardo numbers:
[1, 1, 3, 5, 9, 15, 25, 41, 67, 109, 177, 287, 465, 753, 1219, 1973
 3193, 5167, 8361, 13529, 21891, 35421, 57313, 92735, 150049]

First 25 Fibonacci numbers:
[0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610
 987, 1597, 2584, 4181, 6765, 10946, 17711, 28657, 46368]

Quackery

<lang Quackery> [ 1 1 1 ] is leo ( --> n n n )

 [ 0 1 0 ]             is fibo    (         --> n n n )

 [ 2 1 0 ]             is lucaso (         --> n n n )

 [ temp put 
   rot times 
     [ tuck + 
       temp share + ]
   temp release drop ] is nardo   ( n n n n --> n     )

say "Leonardo numbers:" cr 25 times [ i^ leo nardo echo sp ] cr cr say "Fibonacci numbers:" cr 25 times [ i^ fibo nardo echo sp ] cr cr say "Lucas numbers:" cr 25 times [ i^ lucaso nardo echo sp ]</lang>

Output:

Leonardo numbers:
1 1 3 5 9 15 25 41 67 109 177 287 465 753 1219 1973 3193 5167 8361 13529 21891 35421 57313 92735 150049 

Fibonacci numbers:
0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765 10946 17711 28657 46368 

Lucas numbers:
2 1 3 4 7 11 18 29 47 76 123 199 322 521 843 1364 2207 3571 5778 9349 15127 24476 39603 64079 103682

R

<lang rsplus> leonardo_numbers <- function(add = 1, l0 = 1, l1 = 1, how_many = 25) { result <- c(l0, l1) for (i in 3:how_many) result <- append(result, resulti - 1 + resulti - 2 + add) result } cat("First 25 Leonardo numbers\n") cat(leonardo_numbers(), "\n")

cat("First 25 Leonardo numbers from 0, 1 with add number = 0\n") cat(leonardo_numbers(0, 0, 1), "\n") </lang>

Output:

First 25 Leonardo numbers
1 1 3 5 9 15 25 41 67 109 177 287 465 753 1219 1973 3193 5167 8361 13529 21891 35421 57313 92735 150049 
First 25 Leonardo numbers from 0, 1 with add number = 0
0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765 10946 17711 28657 46368

Racket

<lang racket>#lang racket (define (Leonardo n #:L0 (L0 1) #:L1 (L1 1) #:1+ (1+ 1))

 (cond [(= n 0) L0]
       [(= n 1) L1]
       [else
        (let inr ((n (- n 2)) (L_n-2 L0) (L_n-1 L1))
          (let ((L_n (+ L_n-1 L_n-2 1+)))
            (if (zero? n) L_n (inr (sub1 n) L_n-1 L_n))))]))

(module+ main

 (map Leonardo (range 25))
 (map (curry Leonardo #:L0 0 #:L1 1 #:1+ 0) (range 25)))

(module+ test

 (require rackunit)
 (check-equal? (Leonardo 0) 1)
 (check-equal? (Leonardo 1) 1)
 (check-equal? (Leonardo 2) 3)
 (check-equal? (Leonardo 3) 5))</lang>

Output:

'(1 1 3 5 9 15 25 41 67 109 177 287 465 753 1219 1973 3193 5167 8361 13529 21891 35421 57313 92735 150049)
'(0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765 10946 17711 28657 46368)

Raku

(formerly Perl 6)

<lang perl6>sub 𝑳 ( $𝑳0 = 1, $𝑳1 = 1, $𝑳add = 1 ) { $𝑳0, $𝑳1, { $^n2 + $^n1 + $𝑳add } ... * }

Part 1

say "The first 25 Leonardo numbers:"; put 𝑳()[^25];

Part 2

say "\nThe first 25 numbers using 𝑳0 of 0, 𝑳1 of 1, and adder of 0:"; put 𝑳( 0, 1, 0 )[^25];</lang>

Output:

The first 25 Leonardo numbers:
1 1 3 5 9 15 25 41 67 109 177 287 465 753 1219 1973 3193 5167 8361 13529 21891 35421 57313 92735 150049

The first 25 numbers using 𝑳0 of 0, 𝑳1 of 1, and adder of 0:
0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765 10946 17711 28657 46368

REXX

<lang rexx>/*REXX pgm computes Leonardo numbers, allowing the specification of L(0), L(1), and ADD#*/ numeric digits 500 /*just in case the user gets ka-razy. */ @.=1 /*define the default for the @. array.*/ parse arg N L0 L1 a# . /*obtain optional arguments from the CL*/ if N == | N =="," then N= 25 /*Not specified? Then use the default.*/ if L0\== & L0\=="," then @.0= L0 /*Was " " " " value. */ if L1\== & L1\=="," then @.1= L1 /* " " " " " " */ if a#\== & a#\=="," then @.a= a# /* " " " " " " */ say 'The first ' N " Leonardo numbers are:" /*display a title for the output series*/ if @.0\==1 | @.1\==1 then say 'using ' @.0 " for L(0)" if @.0\==1 | @.1\==1 then say 'using ' @.1 " for L(1)" if @.a\==1 then say 'using ' @.a " for the add number" say /*display blank line before the output.*/ $= /*initialize the output line to "null".*/

            do j=0  for N                       /*construct a list of Leonardo numbers.*/
            if j<2  then z=@.j                  /*for the 1st two numbers, use the fiat*/
                    else do                     /*··· otherwise, compute the Leonardo #*/
                         _=@.0                  /*save the old primary Leonardo number.*/
                         @.0=@.1                /*store the new primary number in old. */
                         @.1=@.0  +  _  +  @.a  /*compute the next Leonardo number.    */
                         z=@.1                  /*store the next Leonardo number in Z. */
                         end                    /* [↑]  only 2 Leonardo #s are stored. */
            $=$ z                               /*append the just computed # to $ list.*/
            end   /*j*/                         /* [↓]  elide the leading blank in  $. */

say strip($) /*stick a fork in it, we're all done. */</lang>

output when using the default input:

The first  25  Leonardo numbers are:

1 1 3 5 9 15 25 41 67 109 177 287 465 753 1219 1973 3193 5167 8361 13529 21891 35421 57313 92735 150049

output when using the input of: 12 0 1 0

The first  25  Leonardo numbers are:
using  0  for L(0)
using  1  for L(1)
using  0  for the  add  number

0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765 10946 17711 28657 46368

Ring

Project : Leanardo numbers

n0 = 1 n1 = 1 add = 1 see "First 25 Leonardo numbers:" + nl leonardo() n0 = 1 n1 = 1 add = 0 see "First 25 Leonardo numbers with L(0) = 0, L(1) = 1, step = 0 (fibonacci numbers):" + nl see "" + add + " " leonardo()

func leonardo()

       see "" + n0 + " " + n1
       for i=3 to 25
             temp=n1
             n1=n0+n1+add
             n0=temp
            see " "+ n1
       next 
       see nl

</lang> Output:

First 25 Leonardo numbers:
1 1 3 5 9 15 25 41 67 109 177 287 465 753 1219 1973 3193 5167 8361 13529 21891 35421 57313 92735 150049
First 25 Leonardo numbers with L(0) = 0, L(1) = 1, step = 0 (fibonacci numbers):
0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765 10946 17711 28657 46368 75025

Ruby

Enumerators are nice for this. <lang ruby>def leonardo(l0=1, l1=1, add=1)

 return to_enum(__method__,l0,l1,add) unless block_given?
 loop do  
   yield l0
   l0, l1 = l1, l0+l1+add
 end

end

p leonardo.take(25) p leonardo(0,1,0).take(25) </lang>

Output:

[1, 1, 3, 5, 9, 15, 25, 41, 67, 109, 177, 287, 465, 753, 1219, 1973, 3193, 5167, 8361, 13529, 21891, 35421, 57313, 92735, 150049]
[0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946, 17711, 28657, 46368]

Run BASIC

<lang Runbasic>sqliteconnect #mem, ":memory:"

mem execute("CREATE TABLE lno (name,L0,L1,ad)")
mem execute("INSERT INTO lno VALUES('Leonardo',1,1,1),('Fibonacci',0,1,0);")
mem execute("SELECT * FROM lno")

for j = 1 to 2

row = #mem #nextrow()

name$ = #row name$() L0 = #row L0() L1 = #row L1() ad = #row ad() print :print name$;" add=";ad :print" ";L0;" ";L1;" "; for i = 3 to 25

 temp  = L1
 L1    = L0 + L1 + ad
 L0    = temp
 print L1;" ";

next i next j end</lang>

Leonardo add=1
 1 1 3 5 9 15 25 41 67 109 177 287 465 753 1219 1973 3193 5167 8361 13529 21891 35421 57313 92735 150049 
Fibonacci add=0
 0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765 10946 17711 28657 46368

Rust

<lang rust>fn leonardo(mut n0: u32, mut n1: u32, add: u32) -> impl std::iter::Iterator<Item = u32> {

   std::iter::from_fn(move || {
       let n = n0;
       n0 = n1;
       n1 += n + add;
       Some(n)
   })

}

fn main() {

   println!("First 25 Leonardo numbers:");
   for i in leonardo(1, 1, 1).take(25) {
       print!("{} ", i);
   }
   println!();
   println!("First 25 Fibonacci numbers:");
   for i in leonardo(0, 1, 0).take(25) {
       print!("{} ", i);
   }
   println!();

}</lang>

Output:

First 25 Leonardo numbers:
1 1 3 5 9 15 25 41 67 109 177 287 465 753 1219 1973 3193 5167 8361 13529 21891 35421 57313 92735 150049 
First 25 Fibonacci numbers:
0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765 10946 17711 28657 46368

Scala

<lang scala>def leo( n:Int, n1:Int=1, n2:Int=1, addnum:Int=1 ) : BigInt = n match {

 case 0 => n1
 case 1 => n2
 case n => leo(n - 1, n1, n2, addnum) + leo(n - 2, n1, n2, addnum) + addnum

}

{ println( "The first 25 Leonardo Numbers:") (0 until 25) foreach { n => print( leo(n) + " " ) }

println( "\n\nThe first 25 Fibonacci Numbers:") (0 until 25) foreach { n => print( leo(n, n1=0, n2=1, addnum=0) + " " ) } } </lang>

Output:

The first 25 Leonardo Numbers:
1 1 3 5 9 15 25 41 67 109 177 287 465 753 1219 1973 3193 5167 8361 13529 21891 35421 57313 92735 150049

The first 25 Fibonacci Numbers:
0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765 10946 17711 28657 46368

Seed7

<lang seed7>$ include "seed7_05.s7i";

const proc: leonardo (in var integer: l0, in var integer: l1, in integer: add, in integer: count) is func

 local
   var integer: temp is 0;
 begin
   for count do
     write(" " <& l0);
     temp := l0 + l1 + add;
     l0 := l1;
     l1 := temp;
   end for;
   writeln;
 end func;

const proc: main is func

 begin
   write("Leonardo Numbers:");
   leonardo(1, 1, 1, 25);
   write("Fibonacci Numbers:");
   leonardo(0, 1, 0, 25);
 end func;</lang>

Output:

Leonardo Numbers: 1 1 3 5 9 15 25 41 67 109 177 287 465 753 1219 1973 3193 5167 8361 13529 21891 35421 57313 92735 150049
Fibonacci Numbers: 0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765 10946 17711 28657 46368

Sidef

<lang ruby>func 𝑳(n, 𝑳0 = 1, 𝑳1 = 1, 𝑳add = 1) {

   { (𝑳0, 𝑳1) = (𝑳1, 𝑳0 + 𝑳1 + 𝑳add) } * n
   return 𝑳0

}

say "The first 25 Leonardo numbers:" say 25.of { 𝑳(_) }

say "\nThe first 25 numbers using 𝑳0 of 0, 𝑳1 of 1, and adder of 0:" say 25.of { 𝑳(_, 0, 1, 0) }</lang>

Output:

The first 25 Leonardo numbers:
[1, 1, 3, 5, 9, 15, 25, 41, 67, 109, 177, 287, 465, 753, 1219, 1973, 3193, 5167, 8361, 13529, 21891, 35421, 57313, 92735, 150049]

The first 25 numbers using 𝑳0 of 0, 𝑳1 of 1, and adder of 0:
[0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946, 17711, 28657, 46368]

Swift

<lang swift>struct Leonardo: Sequence, IteratorProtocol {

   private let add : Int
   private var n0: Int
   private var n1: Int
   
   init(n0: Int = 1, n1: Int = 1, add: Int = 1) {
       self.n0 = n0
       self.n1 = n1
       self.add = add
   }
   
   mutating func next() -> Int? {
       let n = n0
       n0 = n1
       n1 += n + add
       return n
   }

}

print("First 25 Leonardo numbers:") print(Leonardo().prefix(25).map{String($0)}.joined(separator: " "))

print("First 25 Fibonacci numbers:") print(Leonardo(n0: 0, add: 0).prefix(25).map{String($0)}.joined(separator: " "))</lang>

Output:

First 25 Leonardo numbers:
1 1 3 5 9 15 25 41 67 109 177 287 465 753 1219 1973 3193 5167 8361 13529 21891 35421 57313 92735 150049
First 25 Fibonacci numbers:
0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765 10946 17711 28657 46368

VBA

<lang vb> Option Explicit

Private Sub LeonardoNumbers() Dim L, MyString As String

   Debug.Print "First 25 Leonardo numbers :"
   L = Leo_Numbers(25, 1, 1, 1)
   MyString = Join(L, "; ")
   Debug.Print MyString
   Debug.Print "First 25 Leonardo numbers from 0, 1 with add number = 0"
   L = Leo_Numbers(25, 0, 1, 0)
   MyString = Join(L, "; ")
   Debug.Print MyString
   Debug.Print "If the first prarameter is too small :"
   L = Leo_Numbers(1, 0, 1, 0)
   MyString = Join(L, "; ")
   Debug.Print MyString

End Sub

Public Function Leo_Numbers(HowMany As Long, L_0 As Long, L_1 As Long, Add_Nb As Long) Dim N As Long, Ltemp

   If HowMany > 1 Then
       ReDim Ltemp(HowMany - 1)
       Ltemp(0) = L_0: Ltemp(1) = L_1
       For N = 2 To HowMany - 1
            Ltemp(N) = Ltemp(N - 1) + Ltemp(N - 2) + Add_Nb
       Next N
   Else
       ReDim Ltemp(0)
       Ltemp(0) = "The first parameter is too small"
   End If
   Leo_Numbers = Ltemp

End Function </lang>

Output:

First 25 Leonardo numbers :
1; 1; 3; 5; 9; 15; 25; 41; 67; 109; 177; 287; 465; 753; 1219; 1973; 3193; 5167; 8361; 13529; 21891; 35421; 57313; 92735; 150049
First 25 Leonardo numbers from 0, 1 with add number = 0
0; 1; 1; 2; 3; 5; 8; 13; 21; 34; 55; 89; 144; 233; 377; 610; 987; 1597; 2584; 4181; 6765; 10946; 17711; 28657; 46368
If the first prarameter is too small :
The first parameter is too small

Visual Basic .NET

Translation of: C#

<lang vbnet>Module Module1

   Iterator Function Leonardo(Optional L0 = 1, Optional L1 = 1, Optional add = 1) As IEnumerable(Of Integer)
       While True
           Yield L0
           Dim t = L0 + L1 + add
           L0 = L1
           L1 = t
       End While
   End Function

   Sub Main()
       Console.WriteLine(String.Join(" ", Leonardo().Take(25)))
       Console.WriteLine(String.Join(" ", Leonardo(0, 1, 0).Take(25)))
   End Sub

End Module</lang>

Output:

1 1 3 5 9 15 25 41 67 109 177 287 465 753 1219 1973 3193 5167 8361 13529 21891 35421 57313 92735 150049
0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765 10946 17711 28657 46368

Vlang

Translation of: go

<lang vlang>fn leonardo(n int, l0 int, l1 int, add int) []int {

   mut leo := []int{len: n}
   leo[0] = l0
   leo[1] = l1
   for i := 2; i < n; i++ {
       leo[i] = leo[i - 1] + leo[i - 2] + add
   }
   return leo

}

fn main() {

   println("The first 25 Leonardo numbers with L[0] = 1, L[1] = 1 and add number = 1 are:")
   println(leonardo(25, 1, 1, 1))
   println("\nThe first 25 Leonardo numbers with L[0] = 0, L[1] = 1 and add number = 0 are:")
   println(leonardo(25, 0, 1, 0))

}</lang>

Output:

The first 25 Leonardo numbers with L[0] = 1, L[1] = 1 and add number = 1 are:
[1, 1, 3, 5, 9, 15, 25, 41, 67, 109, 177, 287, 465, 753, 1219, 1973, 3193, 5167, 8361, 13529, 21891, 35421, 57313, 92735, 150049]

The first 25 Leonardo numbers with L[0] = 0, L[1] = 1 and add number = 0 are:
[0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946, 17711, 28657, 46368]

Wren

<lang ecmascript>var leonardo = Fn.new { |first, add, limit|

   var leo = List.filled(limit, 0)
   leo[0] = first[0]
   leo[1] = first[1]
   for (i in 2...limit) leo[i] = leo[i-1] + leo[i-2] + add
   return leo

}

System.print("The first 25 Leonardo numbers with L(0) = 1, L(1) = 1 and Add = 1 are:") for (l in leonardo.call([1, 1], 1, 25)) System.write("%(l) ")

System.print("\n\nThe first 25 Leonardo numbers with L(0) = 0, L(1) = 1 and Add = 0 are:") for (l in leonardo.call([0, 1], 0, 25)) System.write("%(l) ") System.print()</lang>

Output:

The first 25 Leonardo numbers with L(0) = 1, L(1) = 1 and Add = 1 are:
1 1 3 5 9 15 25 41 67 109 177 287 465 753 1219 1973 3193 5167 8361 13529 21891 35421 57313 92735 150049 

The first 25 Leonardo numbers with L(0) = 0, L(1) = 1 and Add = 0 are:
0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765 10946 17711 28657 46368

Yabasic

<lang yabasic>limit = 25

sub leonardo(L0, L1, suma, texto$) local i print "Numeros de " + texto$, " (", L0, ",", L1, ",", suma, "):" for i = 1 to limit if i = 1 then print L0, " "; elsif i = 2 then print L1, " "; else print L0 + L1 + suma, " "; tmp = L0 L0 = L1 L1 = tmp + L1 + suma endif next i print chr$(10) end sub

leonardo(1,1,1,"Leonardo") leonardo(0,1,0,"Fibonacci") end</lang>

XPL0

<lang XPL0>int N, L, L0, L1, Add; [Text(0, "Enter L(0), L(1), Add: "); L0:= IntIn(0); L1:= IntIn(0); Add:= IntIn(0); IntOut(0, L0); ChOut(0, ^ ); IntOut(0, L1); ChOut(0, ^ ); for N:= 3 to 25 do

       [L:= L1 + L0 + Add;
       IntOut(0, L);  ChOut(0, ^ );
       L0:= L1;
       L1:= L;
       ];

]</lang>

Output:

Enter L(0), L(1), Add: 1 1 1
1 1 3 5 9 15 25 41 67 109 177 287 465 753 1219 1973 3193 5167 8361 13529 21891 35421 57313 92735 150049 
Enter L(0), L(1), Add: 0 1 0
0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765 10946 17711 28657 46368

zkl

<lang zkl>fcn leonardoNumber(n, n1=1,n2=1,addnum=1){

  if(n==0) return(n1);
  if(n==1) return(n2);
  self.fcn(n-1,n1,n2,addnum) + self.fcn(n-2,n1,n2,addnum) + addnum

}</lang> <lang zkl>println("The first 25 Leonardo Numbers:"); foreach n in (25){ print(leonardoNumber(n)," ") } println("\n");

println("The first 25 Fibonacci Numbers:"); foreach n in (25){ print(leonardoNumber(n, 0,1,0)," ") } println();</lang>

Output:

The first 25 Leonardo Numbers:
1 1 3 5 9 15 25 41 67 109 177 287 465 753 1219 1973 3193 5167 8361 13529 21891 35421 57313 92735 150049 

The first 25 Fibonacci Numbers:
0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765 10946 17711 28657 46368