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A290247
Number of compositions (ordered partitions) of n^3 into cubes.
8
1, 1, 2, 120, 290250, 107320441096, 21715974961480054078, 8487986089807555456140271121440, 22615863021403796876556069287242400147213424924, 1449638083412288206280215383952017948209203861522683138464747658192
OFFSET
0,3
FORMULA
a(n) = [x^(n^3)] 1/(1 - Sum_{k>=1} x^(k^3)).
a(n) = A023358(A000578(n)).
EXAMPLE
a(2) = 2 because 2^3 = 8 and we have [8], [1, 1, 1, 1, 1, 1, 1, 1].
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}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Jul 24 2017
STATUS
approved