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

Author

Ilya Gutkovskiy, Dec 01 2020

Keywords

• nonn

Examples

			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].
		

Links

• Index entries for sequences related to partitions
• Index entries for sequences related to sums of cubes

Crossrefs

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

Programs

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]

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.