A340981 Number of ways to write n as an ordered sum of 8 positive cubes.

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

Author

Ilya Gutkovskiy, Feb 01 2021

Keywords

• nonn
• look

Links

• Robert Israel, Table of n, a(n) for n = 8..10000
• Index entries for sequences related to sums of cubes

Crossrefs

Cf. A000578, A010057, A025461, A051344, A173681, A280618, A340977, A340978, A340979, A340980, A340982, A340983.

Programs

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] &

Formula

G.f.: (Sum_{k>=1} x^(k^3))^8.