A340980 Number of ways to write n as an ordered sum of 7 positive cubes.

1, 0, 0, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0, 0, 21, 0, 0, 0, 0, 0, 0, 35, 0, 0, 0, 0, 7, 0, 35, 0, 0, 0, 0, 42, 0, 21, 0, 0, 0, 0, 105, 0, 7, 0, 0, 0, 0, 140, 0, 1, 0, 0, 21, 0, 105, 0, 0, 0, 0, 105, 0, 42, 0, 7, 0, 0, 210, 0, 7, 0, 42, 0, 0, 210, 0, 0, 0, 105, 35, 0, 105, 0, 0, 0, 140, 140, 0, 21, 0, 42

Offset

7,8

Links

Robert Israel, Table of n, a(n) for n = 7..10000

Index entries for sequences related to sums of cubes

Formula

G.f.: (Sum_{k>=1} x^(k^3))^7.

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, 7):
seq(a(n), n=7..96);  # Alois P. Heinz, Feb 01 2021

Mathematica

nmax = 96; CoefficientList[Series[Sum[x^(k^3), {k, 1, Floor[nmax^(1/3)] + 1}]^7, {x, 0, nmax}], x] // Drop[#, 7] &

Crossrefs

Cf. A000578, A010057, A025460, A051344, A173676, A280618, A340977, A340978, A340979, A340981, A340982, A340983.

Sequence in context: A115528 A354995 A270032 * A305671 A228633 A106226

Adjacent sequences: A340977 A340978 A340979 * A340981 A340982 A340983

Keyword

nonn

Author

Ilya Gutkovskiy, Feb 01 2021

Status

approved