A339368 Number of partitions of n into an even number of cubes.

1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 2, 2, 2, 3, 2, 3, 2, 4, 2, 4, 3, 4, 3, 4, 3, 4, 4, 4, 4, 5, 4, 5, 4, 6, 4, 6, 5, 6, 5, 7, 5, 7, 6, 7, 6, 8, 6, 8, 7, 9, 8, 9, 9, 9, 9, 10, 9, 11, 10, 11, 10, 12, 10, 12, 11, 13, 12, 14, 13, 14, 13

Offset

0,17

Links

Table of n, a(n) for n=0..85.

Index entries for sequences related to partitions

Index entries for sequences related to sums of cubes

Formula

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

a(n) = (A003108(n) + A292560(n)) / 2.

Example

a(16) = 2 because we have [8, 8] and [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1].

Mathematica

nmax = 85; CoefficientList[Series[(1/2) (Product[1/(1 - x^(k^3)), {k, 1, Floor[nmax^(1/3)] + 1}] + Product[1/(1 + x^(k^3)), {k, 1, Floor[nmax^(1/3)] + 1}]), {x, 0, nmax}], x]

Crossrefs

Cf. A000578, A003108, A027187, A292560, A339364, A339369.

Sequence in context: A175096 A111627 A008618 * A225572 A318471 A161234

Adjacent sequences: A339365 A339366 A339367 * A339369 A339370 A339371

Keyword

nonn

Author

Ilya Gutkovskiy, Dec 01 2020

Status

approved