A280351 Expansion of Sum_{k>=0} (x/(1 - x))^(k^3).

1, 1, 1, 1, 1, 1, 1, 1, 2, 9, 37, 121, 331, 793, 1717, 3433, 6436, 11441, 19449, 31825, 50389, 77521, 116281, 170545, 245158, 346105, 480701, 657802, 888058, 1184419, 1564435, 2063206, 2799487, 4272049, 8544097, 23535821, 77331981, 262534537, 865287625, 2720095405

Offset

0,9

Comments

Number of compositions of n into a cube number of parts.

Links

Table of n, a(n) for n=0..39.

Index entries for sequences related to compositions

Formula

a(0) = 1; a(n) = Sum_{k=1..floor(n^(1/3))} binomial(n-1, k^3-1) for n > 0. - Jerzy R Borysowicz, Dec 22 2022

Example

a(9) = 9 because we have:
[1]  [9]
[2]  [2, 1, 1, 1, 1, 1, 1, 1]
[3]  [1, 2, 1, 1, 1, 1, 1, 1]
[4]  [1, 1, 2, 1, 1, 1, 1, 1]
[5]  [1, 1, 1, 2, 1, 1, 1, 1]
[6]  [1, 1, 1, 1, 2, 1, 1, 1]
[7]  [1, 1, 1, 1, 1, 2, 1, 1]
[8]  [1, 1, 1, 1, 1, 1, 2, 1]
[9]  [1, 1, 1, 1, 1, 1, 1, 2]

Maple

a := n -> ifelse(n = 0, 1, add(binomial(n - 1, k^3 - 1), k = 1..floor(n^(1/3)))):
seq(a(n), n = 0..39); # Peter Luschny, Dec 23 2022

Mathematica

nmax = 39; CoefficientList[Series[Sum[(x/(1 - x))^k^3, {k, 0, nmax}], {x, 0, nmax}], x]

Crossrefs

Cf. A000578, A052467, A103198, A280352.

Sequence in context: A111601 A328268 A330346 * A306721 A306852 A275425

Adjacent sequences: A280348 A280349 A280350 * A280352 A280353 A280354

Keyword

nonn,easy

Author

Ilya Gutkovskiy, Jan 01 2017

Extensions

a(0)=1 prepended by Alois P. Heinz, Dec 17 2022

Status

approved