OFFSET
1,2
COMMENTS
Total number of parts in all compositions (ordered partitions) of n into cubes (A000578).
LINKS
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
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Jan 30 2017
STATUS
approved