cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A327448 Number of ways the first n cubes can be partitioned into three sets with equal sums.

Original entry on oeis.org

1, 0, 0, 691, 3416, 0, 233, 1168, 0, 8857, 18157, 0, 2176512, 3628118, 0, 3204865, 8031495, 0, 79514209, 205927212, 0, 5152732369, 13493840291, 0
Offset: 23

Views

Author

N. J. A. Sloane, Sep 19 2019

Keywords

Comments

Note the offset.

Examples

			The unique smallest solution (for n = 23) is
27 + 216 + 1000 + 2197 + 5832 + 6859 + 9261 =
1 + 64 + 343 + 512 + 1728 + 4096 + 8000 + 10648 =
8 + 125 + 729 + 1331 + 2744 + 3375 + 4913 + 12167.
		

References

  • Keith F. Lynch, Posting to Math Fun Mailing List, Sep 17 2019.

Crossrefs

Programs

  • Maple
    s:= proc(n) option remember; `if`(n<2, 0, n^3+s(n-1)) end:
    b:= proc(n, x, y) option remember; `if`(n=1, 1, (p-> (l->
          add(`if`(p>l[i], 0, b(n-1, sort(subsop(i=l[i]-p, l))
                [1..2][])), i=1..3))([x, y, s(n)-x-y]))(n^3))
        end:
    a:= n-> `if`(irem(1+s(n), 3, 'q')=0, b(n, q-1, q)/2, 0):
    seq(a(n), n=23..27);  # Alois P. Heinz, Sep 30 2019
  • Mathematica
    s[n_] := s[n] = If[n < 2, 0, n^3 + s[n - 1]];
    b[n_, x_, y_] := b[n, x, y] = If[n == 1, 1, With[{p = n^3}, Sum[If[p > #[[i]], 0, b[n - 1, Sequence @@ Sort[ReplacePart[#, i -> #[[i]] - p]][[1 ;; 2]]]], {i, 1, 3}]]&[{x, y, s[n] - x - y}]];
    a[n_] := a[n] = If[q = Quotient[1 + s[n], 3]; Mod[1 + s[n], 3] == 0, b[n, q - 1, q]/2, 0];
    Table[Print[n, " ", a[n]]; a[n], {n, 23, 34}] (* Jean-François Alcover, Nov 08 2020, after Alois P. Heinz *)

Formula

a(n) > 0 => n in { A007494 }. - Alois P. Heinz, Sep 30 2019

Extensions

a(32), a(33), a(35) recomputed and a(36)-a(38) added by Alois P. Heinz, Sep 30 2019
a(39)-a(46) from Bert Dobbelaere, May 15 2021