A259792 Number of partitions of n^3 into cubes.

1, 1, 2, 5, 17, 62, 258, 1050, 4365, 18012, 73945, 301073, 1214876, 4852899, 19187598, 75070201, 290659230, 1113785613, 4224773811, 15866483556, 59011553910, 217410395916, 793635925091, 2871246090593, 10297627606547, 36620869115355, 129166280330900

Offset

0,3

Links

Alois P. Heinz and Vaclav Kotesovec, Table of n, a(n) for n = 0..173 (terms 0..120 from Alois P. Heinz)

H. L. Fisher, Letter to N. J. A. Sloane, Mar 16 1989

G. H. Hardy and S. Ramanujan, Asymptotic formulae in combinatory analysis, Proceedings of the London Mathematical Society, 2, XVI, 1917, p. 373.

Formula

a(n) = [x^(n^3)] Product_{j>=1} 1/(1-x^(j^3)). - Alois P. Heinz, Jul 10 2015

a(n) = A003108(n^3). - Vaclav Kotesovec, Aug 19 2015

a(n) ~ exp(4 * (Gamma(1/3)*Zeta(4/3))^(3/4) * n^(3/4) / 3^(3/2)) * (Gamma(1/3)*Zeta(4/3))^(3/4) / (24*Pi^2*n^(15/4)) [after Hardy & Ramanujan, 1917]. - Vaclav Kotesovec, Dec 29 2016

Maple

b:= proc(n, i) option remember; `if`(n=0 or i=1, 1,
      b(n, i-1) +`if`(i^3>n, 0, b(n-i^3, i)))
    end:
a:= n-> b(n^3, n):
seq(a(n), n=0..26);  # Alois P. Heinz, Jul 10 2015

Mathematica

$RecursionLimit = 1000; b[n_, i_] := b[n, i] = If[n==0 || i==1, 1, b[n, i-1] + If[ i^3>n, 0, b[n-i^3, i]]]; a[n_] := b[n^3, n]; Table[a[n], {n, 0, 26}] (* Jean-François Alcover, Jul 15 2015, after Alois P. Heinz *)

Crossrefs

A row of the array in A259799.

Cf. A279329.

Cf. A001156, A003108, A046042.

Cf. A037444, A259793.

Sequence in context: A112832 A148415 A148416 * A003456 A109084 A217596

Adjacent sequences: A259789 A259790 A259791 * A259793 A259794 A259795

Keyword

nonn

Author

N. J. A. Sloane, Jul 06 2015

Extensions

More term from Alois P. Heinz, Jul 10 2015

Status

approved