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A340982
Number of ways to write n as an ordered sum of 9 positive cubes.
8
1, 0, 0, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0, 0, 36, 0, 0, 0, 0, 0, 0, 84, 0, 0, 0, 0, 9, 0, 126, 0, 0, 0, 0, 72, 0, 126, 0, 0, 0, 0, 252, 0, 84, 0, 0, 0, 0, 504, 0, 36, 0, 0, 36, 0, 630, 0, 9, 0, 0, 252, 0, 504, 0, 10, 0, 0, 756, 0, 252, 0, 72, 0, 0, 1260, 0, 72, 0, 252, 84, 0, 1260, 0, 9, 0, 504, 504
OFFSET
9,8
FORMULA
G.f.: (Sum_{k>=1} x^(k^3))^9.
MAPLE
b:= proc(n, t) option remember;
`if`(n=0, `if`(t=0, 1, 0), `if`(t<1, 0, add((s->
`if`(s>n, 0, b(n-s, t-1)))(j^3), j=1..iroot(n, 3))))
end:
a:= n-> b(n, 9):
seq(a(n), n=9..94); # Alois P. Heinz, Feb 01 2021
MATHEMATICA
nmax = 94; CoefficientList[Series[Sum[x^(k^3), {k, 1, Floor[nmax^(1/3)] + 1}]^9, {x, 0, nmax}], x] // Drop[#, 9] &
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Feb 01 2021
STATUS
approved