A340982 Number of ways to write n as an ordered sum of 9 positive cubes.

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

Links

Robert Israel, Table of n, a(n) for n = 9..10000

Index entries for sequences related to sums of cubes

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] &

Crossrefs

Cf. A000578, A010057, A025462, A051344, A173682, A280618, A340977, A340978, A340979, A340980, A340981, A340983.

Sequence in context: A228635 A229660 A306757 * A334624 A036483 A353803

Adjacent sequences: A340979 A340980 A340981 * A340983 A340984 A340985

Keyword

nonn

Author

Ilya Gutkovskiy, Feb 01 2021

Status

approved