A339369 Number of partitions of n into an odd number of cubes.

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

Offset

0,18

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(17) = 2 because we have [8, 8, 1] and [1, 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, A027193, A292560, A339365, A339368.

Sequence in context: A127267 A268173 A008617 * A025824 A230037 A211262

Adjacent sequences: A339366 A339367 A339368 * A339370 A339371 A339372

Keyword

nonn

Author

Ilya Gutkovskiy, Dec 01 2020

Status

approved