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A340978
Number of ways to write n as an ordered sum of 5 positive cubes.
9
1, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 10, 0, 0, 0, 0, 0, 0, 10, 0, 0, 0, 0, 5, 0, 5, 0, 0, 0, 0, 20, 0, 1, 0, 0, 0, 0, 30, 0, 0, 0, 0, 0, 0, 20, 0, 0, 0, 0, 10, 0, 5, 0, 0, 0, 0, 30, 0, 0, 0, 5, 0, 0, 30, 0, 0, 0, 20, 0, 0, 10, 0, 0, 0, 30, 10, 0, 0, 0, 0, 0, 20, 20, 0, 0, 0, 20, 0, 5, 10
OFFSET
5,8
FORMULA
G.f.: (Sum_{k>=1} x^(k^3))^5.
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, 5):
seq(a(n), n=5..97); # Alois P. Heinz, Feb 01 2021
MATHEMATICA
nmax = 97; CoefficientList[Series[Sum[x^(k^3), {k, 1, Floor[nmax^(1/3)] + 1}]^5, {x, 0, nmax}], x] // Drop[#, 5] &
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Feb 01 2021
STATUS
approved