A340983 Number of ways to write n as an ordered sum of 10 positive cubes.

1, 0, 0, 0, 0, 0, 0, 10, 0, 0, 0, 0, 0, 0, 45, 0, 0, 0, 0, 0, 0, 120, 0, 0, 0, 0, 10, 0, 210, 0, 0, 0, 0, 90, 0, 252, 0, 0, 0, 0, 360, 0, 210, 0, 0, 0, 0, 840, 0, 120, 0, 0, 45, 0, 1260, 0, 45, 0, 0, 360, 0, 1260, 0, 20, 0, 0, 1260, 0, 840, 0, 91, 0, 0, 2520, 0, 360, 0, 360, 120, 0, 3150, 0, 90

Offset

10,8

Links

Robert Israel, Table of n, a(n) for n = 10..10000

Index entries for sequences related to sums of cubes

Formula

G.f.: (Sum_{k>=1} x^(k^3))^10.

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, 10):
seq(a(n), n=10..92);  # Alois P. Heinz, Feb 01 2021

Mathematica

nmax = 92; CoefficientList[Series[Sum[x^(k^3), {k, 1, Floor[nmax^(1/3)] + 1}]^10, {x, 0, nmax}], x] // Drop[#, 10] &

Crossrefs

Cf. A000578, A010057, A025463, A051344, A280618, A340977, A340978, A340979, A340980, A340981, A340982.

Sequence in context: A270035 A228636 A306758 * A247118 A010894 A002045

Adjacent sequences: A340980 A340981 A340982 * A340984 A340985 A340986

Keyword

nonn,look

Author

Ilya Gutkovskiy, Feb 01 2021

Status

approved