A339421 Number of compositions (ordered partitions) of n into an odd number of cubes.

0, 1, 0, 1, 0, 1, 0, 1, 1, 1, 3, 1, 5, 1, 7, 1, 9, 4, 11, 11, 13, 22, 15, 37, 18, 56, 29, 80, 56, 109, 107, 142, 190, 184, 313, 255, 490, 391, 731, 644, 1045, 1082, 1458, 1792, 2044, 2895, 2957, 4531, 4463, 6863, 6972, 10126, 11090, 14739, 17691, 21484, 27954, 31741

Offset

0,11

Links

Alois P. Heinz, Table of n, a(n) for n = 0..5000

Index entries for sequences related to compositions

Index entries for sequences related to sums of cubes

Formula

G.f.: (1/2) * (1 / (1 - Sum_{k>=1} x^(k^3)) - 1 / Sum_{k>=0} x^(k^3)).

a(n) = (A023358(n) - A323633(n)) / 2.

a(n) = -Sum_{k=0..n-1} A023358(k) * A323633(n-k).

Example

a(10) = 3 because we have [8, 1, 1], [1, 8, 1] and [1, 1, 8].

Maple

b:= proc(n, t) option remember; local r, f, g;
      if n=0 then t else r, f, g:=$0..2; while f<=n
      do r, f, g:= r+b(n-f, 1-t), f+3*g*(g-1)+1, g+1 od; r fi
    end:
a:= n-> b(n, 0):
seq(a(n), n=0..60);  # Alois P. Heinz, Dec 03 2020

Mathematica

nmax = 57; CoefficientList[Series[(1/2) (1/(1 - Sum[x^(k^3), {k, 1, Floor[nmax^(1/3)] + 1}]) - 1/Sum[x^(k^3), {k, 0, Floor[nmax^(1/3)] + 1}]), {x, 0, nmax}], x]

Crossrefs

Cf. A000578, A023358, A166444, A323633, A339369, A339419, A339420.

Sequence in context: A340086 A307153 A378513 * A336898 A300330 A328478

Adjacent sequences: A339418 A339419 A339420 * A339422 A339423 A339424

Keyword

nonn

Author

Ilya Gutkovskiy, Dec 03 2020

Status

approved