A025463 Number of partitions of n into 10 positive cubes.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 2, 0, 0, 1, 0, 1, 0, 2, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 2, 0, 1, 1, 0, 1, 0, 1, 0

Offset

0,74

Links

Alois P. Heinz, Table of n, a(n) for n = 0..65536

Index entries for sequences related to sums of cubes

Formula

a(n) = [x^n y^10] Product_{k>=1} 1/(1 - y*x^(k^3)). - Ilya Gutkovskiy, Apr 23 2019

Maple

b:= proc(n, i, t) option remember; `if`(n=0, `if`(t=0, 1, 0),
      `if`(i<1 or t<1, 0, b(n, i-1, t)+
      `if`(i^3>n, 0, b(n-i^3, i, t-1))))
    end:
a:= n-> b(n, iroot(n, 3), 10):
seq(a(n), n=0..120);  # Alois P. Heinz, Dec 21 2018

Mathematica

b[n_, i_, t_] := b[n, i, t] = If[n == 0, If[t == 0, 1, 0], If[i < 1 || t < 1, 0, b[n, i - 1, t] + If[i^3 > n, 0, b[n - i^3, i, t - 1]]]];
a[n_] := b[n, n^(1/3) // Floor, 10];
a /@ Range[0, 120] (* Jean-François Alcover, Dec 04 2020, after Alois P. Heinz *)

Crossrefs

Cf. A000578 (cubes).

Column k=10 of A320841.

Sequence in context: A366092 A086965 A256572 * A327686 A274472 A283669

Adjacent sequences: A025460 A025461 A025462 * A025464 A025465 A025466

Keyword

nonn

Author

David W. Wilson

Status

approved