Riordan numbers: Difference between revisions
Add PARI/GP implementation
(→{{header|Bracmat}}: Added a solution.) |
(Add PARI/GP implementation) |
||
| (2 intermediate revisions by the same user not shown) | |||
Line 994:
834,086,421 2,358,641,376 6,684,761,125 18,985,057,351
54,022,715,451 154,000,562,758 439,742,222,071 1,257,643,249,140
</pre>
=={{header|Mathematica}}/{{header|Wolfram Language}}==
<syntaxhighlight lang="Mathematica">
Riordan[N_] :=
Module[{a = {1, 0, 1}},
Do[AppendTo[a, ((n - 1) (2 a[[n]] + 3 a[[n - 1]])/(n + 1))], {n, 3,
N}];
a]
rios = Riordan[10000];
Do[Print[ToString@NumberForm[rios[[i]], DigitBlock -> 3]], {i, 32}]
Print["The 1,000th Riordan number has ", IntegerLength[rios[[1000]]],
" digits."];
Print["The 10,000th Riordan number has ",
IntegerLength[rios[[10000]]], " digits."];
</syntaxhighlight>
{{out}}
<pre>
1
0
1
1
3
6
15
36
91
232
603
1,585
4,213
11,298
30,537
83,097
227,475
625,992
1,730,787
4,805,595
13,393,689
37,458,330
105,089,229
295,673,994
834,086,421
2,358,641,376
6,684,761,125
18,985,057,351
54,022,715,451
154,000,562,758
439,742,222,071
1,257,643,249,140
The 1,000th Riordan number has 472 digits.
The 10,000th Riordan number has 4765 digits.
</pre>
Line 1,061 ⟶ 1,117:
<pre>The 1000th Riordan number has 472 digits.
The 10000th Riordan number has 4765 digits.
</pre>
=={{header|PARI/GP}}==
<syntaxhighlight lang="PARI/GP">
\\ Increase the stack size if necessary
default(parisize, "32M"); \\ Increase to 32MB, adjust if necessary
Riordan(N) = {
my(a = vector(N));
a[1] = 1; a[2] = 0; a[3] = 1;
for (n = 3, N-1,
a[n+1] = ((n - 1) * (2 * a[n] + 3 * a[n-1]) \ (n + 1)); \\ Integer division
);
return(a);
}
rios = Riordan(10000);
\\ Now print the first 32 elements in the desired format
for (i = 1, 32,{
print1(rios[i]," ")
});
print("")
\\ Print the number of digits for the 1000th and 10000th Riordan numbers
print("The 1,000th Riordan has ", #digits(rios[1000]), " digits.");
print("The 10,000th Riordan has ", #digits(rios[10000]), " digits.");
</syntaxhighlight>
{{out}}
<pre>
1 0 1 1 3 6 15 36 91 232 603 1585 4213 11298 30537 83097 227475 625992 1730787 4805595 13393689 37458330 105089229 295673994 834086421 2358641376 6684761125 18985057351 54022715451 154000562758 439742222071 1257643249140
The 1,000th Riordan has 472 digits.
The 10,000th Riordan has 4765 digits.
</pre>
Line 1,587 ⟶ 1,677:
1: { #1d #0d #1d #1d #3d #6d #15d #36d #91d #232d #603d #1585d #4213d 11298d #30537d #83097d #227475d #625992d #1730787d #4805595d #13393689d #37458330d #105089229d #295673994d #834086421d #2358641376d #6684761125d #18985057351d #54022715451d #154000562758d #439742222071d #1257643249140d }
</pre>
=={{header|Scala}}==
{{trans|Java}}
<syntaxhighlight lang="Scala">
import java.math.BigInteger
import scala.collection.mutable.ArrayBuffer
object RiordanNumbers extends App {a
val limit = 10000
val THREE = BigInteger.valueOf(3)
val riordans: ArrayBuffer[BigInteger] = ArrayBuffer.fill(limit)(BigInteger.ZERO)
riordans(0) = BigInteger.ONE
riordans(1) = BigInteger.ZERO
for (n <- 2 until limit) {
val term = BigInteger.TWO.multiply(riordans(n - 1)).add(THREE.multiply(riordans(n - 2)))
riordans(n) = BigInteger.valueOf(n - 1).multiply(term).divide(BigInteger.valueOf(n + 1))
}
println("The first 32 Riordan numbers:")
for (i <- 0 until 32) {
print(f"${riordans(i)}%14d")
if (i % 4 == 3) println()
else print(" ")
}
println()
List(1000, 10000).foreach { count =>
val length = riordans(count - 1).toString.length
println(s"The ${count}th Riordan number has $length digits")
}
}
</syntaxhighlight>
{{out}}
<pre>
The first 32 Riordan numbers:
1 0 1 1
3 6 15 36
91 232 603 1585
4213 11298 30537 83097
227475 625992 1730787 4805595
13393689 37458330 105089229 295673994
834086421 2358641376 6684761125 18985057351
54022715451 154000562758 439742222071 1257643249140
The 1000th Riordan number has 472 digits
The 10000th Riordan number has 4765 digits
</pre>
=={{header|SETL}}==
| |||