A290247 Number of compositions (ordered partitions) of n^3 into cubes.

1, 1, 2, 120, 290250, 107320441096, 21715974961480054078, 8487986089807555456140271121440, 22615863021403796876556069287242400147213424924, 1449638083412288206280215383952017948209203861522683138464747658192

Offset: 0

Author

Ilya Gutkovskiy, Jul 24 2017

Keywords

• nonn

Examples

			a(2) = 2 because 2^3 = 8 and we have [8], [1, 1, 1, 1, 1, 1, 1, 1].
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..22
• Index entries for sequences related to compositions

Crossrefs

Cf. A000578, A023358, A030272, A224366, A259792.

Programs

Maple

b:= proc(n) option remember; local i; if n=0 then 1
      else 0; for i while i^3<=n do %+b(n-i^3) od fi
    end:
a:= n-> b(n^3):
seq(a(n), n=0..10);  # Alois P. Heinz, Aug 12 2017

Mathematica

Table[SeriesCoefficient[1/(1 - Sum[x^k^3, {k, 1, n}]), {x, 0, n^3}], {n, 0, 9}]

Formula

a(n) = [x^(n^3)] 1/(1 - Sum_{k>=1} x^(k^3)).

a(n) = A023358(A000578(n)).