Sum of first n cubes

Sum of first n cubes is a draft programming task. It is not yet considered ready to be promoted as a complete task, for reasons that should be found in its talk page.

Task

Find and show sum of first   n   cubes,   where n < 51

Factor

Works with: Factor version 0.99 2021-02-05

<lang factor>USING: grouping math math.functions prettyprint sequences ;

50 <iota> 0 [ 3 ^ + ] accumulate* 10 group simple-table.</lang>

Output:

0      1      9      36     100    225     441     784     1296    2025
3025   4356   6084   8281   11025  14400   18496   23409   29241   36100
44100  53361  64009  76176  90000  105625  123201  142884  164836  189225
216225 246016 278784 314721 354025 396900  443556  494209  549081  608400
672400 741321 815409 894916 980100 1071225 1168561 1272384 1382976 1500625

Alternatively, this is the same as the triangular numbers squared, where the triangular numbers are given by

T_n = n(n + 1) / 2

Works with: Factor version 0.99 2021-02-05

<lang factor>USING: grouping kernel math prettyprint sequences ;

triangular ( n -- m ) dup 1 + * 2/ ;

50 <iota> [ triangular sq ] map 10 group simple-table.</lang>

Output:

As above.

Raku

<lang perl6>my @sums_of_all_cubes = [\+] ^Inf X** 3;

say .fmt('%7d') for @sums_of_all_cubes.head(50).batch(10);</lang>

Output:

     0       1       9      36     100     225     441     784    1296    2025
  3025    4356    6084    8281   11025   14400   18496   23409   29241   36100
 44100   53361   64009   76176   90000  105625  123201  142884  164836  189225
216225  246016  278784  314721  354025  396900  443556  494209  549081  608400
672400  741321  815409  894916  980100 1071225 1168561 1272384 1382976 1500625

REXX

<lang rexx>/*REXX program finds and displays a number of sums of the first N cubes. */ parse arg lo hi cols . /*obtain optional argument from the CL.*/ if hi== | hi=="," then hi= 50 /*Not specified? Then use the default.*/ if cols== | cols=="," then cols= 10 /* " " " " " " */ w= 12 /*width of a number in any column. */

                    @cubeSum= ' cube sums,  where  N  < '     commas(hi)

say ' index │'center(@cubeSum, 1 + cols*(w+1) ) say '───────┼'center("" , 1 + cols*(w+1), '─') found= 0; idx= 1 /*initialize the number for the index. */ $=; sum= 0 /*a list of the sum of N cubes. . */

    do j=0  for hi;       sum= sum + j**3       /*compute the sum of this cube + others*/
    found= found + 1                            /*bump the number of  sums  shown.     */
    c= commas(sum)                              /*maybe add commas to the number.      */
    $= $ right(c, max(w, length(c) ) )          /*add a sum of  N  cubes to the $ list.*/
    if found//cols\==0  then iterate            /*have we populated a line of output?  */
    say center(idx, 7)'│'  substr($, 2);   $=   /*display what we have so far  (cols). */
    idx= idx + cols                             /*bump the  index  count for the output*/
    end   /*j*/

if $\== then say center(idx, 7)"│" substr($, 2) /*possible display residual output.*/ say '───────┴'center("" , 1 + cols*(w+1), '─') say say 'Found ' commas(found) @cubeSum exit 0 /*stick a fork in it, we're all done. */ /*──────────────────────────────────────────────────────────────────────────────────────*/ commas: parse arg ?; do jc=length(?)-3 to 1 by -3; ?=insert(',', ?, jc); end; return ?</lang>

output   when using the default inputs:

(Shown at five-sixth size.)

 index │                                                    cube sums,  where  N  <  50
───────┼───────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────
   1   │            0            1            9           36          100          225          441          784        1,296        2,025
  11   │        3,025        4,356        6,084        8,281       11,025       14,400       18,496       23,409       29,241       36,100
  21   │       44,100       53,361       64,009       76,176       90,000      105,625      123,201      142,884      164,836      189,225
  31   │      216,225      246,016      278,784      314,721      354,025      396,900      443,556      494,209      549,081      608,400
  41   │      672,400      741,321      815,409      894,916      980,100    1,071,225    1,168,561    1,272,384    1,382,976    1,500,625
───────┴───────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────

Ring

<lang ring> see "working..." + nl see "Sum of first n cubes:" + nl row = 0 lenCubes = 50

for n = 1 to lenCubes

   sumCubes = 0
   for m = 1 to n
       sumCubes = sumCubes + pow(m,3)
   next
   row = row + 1
   see "" + sumCubes + " "
   if row%5 = 0
      see nl
   ok    

next

see "Found " + row + " cubes" + nl see "done..." + nl </lang>

Output:

working...
Sum of first n cubes:
1 9 36 100 225 
441 784 1296 2025 3025 
4356 6084 8281 11025 14400 
18496 23409 29241 36100 44100 
53361 64009 76176 90000 105625 
123201 142884 164836 189225 216225 
246016 278784 314721 354025 396900 
443556 494209 549081 608400 672400 
741321 815409 894916 980100 1071225 
1168561 1272384 1382976 1500625 1625625 
Found 50 cubes
done...