OFFSET
0,9
COMMENTS
Number of compositions of n into a cube number of parts.
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
KEYWORD
nonn,easy
AUTHOR
Ilya Gutkovskiy, Jan 01 2017
EXTENSIONS
a(0)=1 prepended by Alois P. Heinz, Dec 17 2022
STATUS
approved