A281809 Expansion of Sum_{i>=1} x^(i^3) / (1 - Sum_{j>=1} x^(j^3))^2.

1, 2, 3, 4, 5, 6, 7, 9, 13, 19, 27, 37, 49, 63, 79, 99, 126, 163, 213, 279, 364, 471, 603, 766, 970, 1229, 1562, 1992, 2545, 3251, 4144, 5266, 6672, 8435, 10655, 13462, 17019, 21527, 27230, 34425, 43478, 54846, 69114, 87032, 109555, 137889, 173543, 218393, 274765, 345544, 434332, 545650, 685187, 860105, 1079402

Offset

1,2

Comments

Total number of parts in all compositions (ordered partitions) of n into cubes (A000578).

Links

Alois P. Heinz, Table of n, a(n) for n = 1..10919

Index entries for sequences related to sums of cubes

Index entries for sequences related to compositions

Formula

G.f.: Sum_{i>=1} x^(i^3) / (1 - Sum_{j>=1} x^(j^3))^2.

Example

a(10) = 19 because we have [8, 1, 1], [1, 8, 1], [1, 1, 8], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1] and 3 + 3 + 3 + 10 = 19.

Maple

b:= proc(n) option remember; `if`(n=0, [1, 0], add(
      (p-> p+[0, p[1]])(b(n-j^3)), j=1..iroot(n, 3)))
    end:
a:= n-> b(n)[2]:
seq(a(n), n=1..55);  # Alois P. Heinz, Aug 07 2019

Mathematica

nmax = 55; Rest[CoefficientList[Series[Sum[x^i^3, {i, 1, nmax}]/(1 - Sum[x^j^3, {j, 1, nmax}])^2, {x, 0, nmax}], x]]

Crossrefs

Cf. A000578, A023358.

Sequence in context: A322801 A322798 A085793 * A143286 A160339 A033072

Adjacent sequences: A281806 A281807 A281808 * A281810 A281811 A281812

Keyword

nonn

Author

Ilya Gutkovskiy, Jan 30 2017

Status

approved