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A340981
Number of ways to write n as an ordered sum of 8 positive cubes.
8
1, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 28, 0, 0, 0, 0, 0, 0, 56, 0, 0, 0, 0, 8, 0, 70, 0, 0, 0, 0, 56, 0, 56, 0, 0, 0, 0, 168, 0, 28, 0, 0, 0, 0, 280, 0, 8, 0, 0, 28, 0, 280, 0, 1, 0, 0, 168, 0, 168, 0, 8, 0, 0, 420, 0, 56, 0, 56, 0, 0, 560, 0, 8, 0, 168, 56, 0, 420, 0, 0, 0, 280, 280, 0, 168
OFFSET
8,8
FORMULA
G.f.: (Sum_{k>=1} x^(k^3))^8.
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, 8):
seq(a(n), n=8..95); # Alois P. Heinz, Feb 01 2021
MATHEMATICA
nmax = 95; CoefficientList[Series[Sum[x^(k^3), {k, 1, Floor[nmax^(1/3)] + 1}]^8, {x, 0, nmax}], x] // Drop[#, 8] &
KEYWORD
nonn,look
AUTHOR
Ilya Gutkovskiy, Feb 01 2021
STATUS
approved