A035385 Number of partitions of n into parts 6k+2 or 6k+4.

1, 0, 1, 0, 2, 0, 2, 0, 4, 0, 5, 0, 7, 0, 9, 0, 13, 0, 16, 0, 22, 0, 27, 0, 36, 0, 44, 0, 57, 0, 70, 0, 89, 0, 108, 0, 135, 0, 163, 0, 202, 0, 243, 0, 297, 0, 355, 0, 431, 0, 513, 0, 617, 0, 731, 0, 874, 0, 1031, 0, 1225, 0, 1439, 0, 1701, 0, 1991, 0, 2341, 0, 2731, 0, 3197, 0

Offset

0,5

Links

Table of n, a(n) for n=0..73.

Formula

a(2*n) = A000726(n). a(2*n + 1) = 0. - Michael Somos, Jun 02 2012

If n is even, a(n) ~ exp(Pi*sqrt(2*n)/3) / (3 * 2^(1/4) * n^(3/4)). - Vaclav Kotesovec, Aug 27 2015

Mathematica

nmax = 100; CoefficientList[Series[Product[1/((1 - x^(6k+2))*(1 - x^(6k+4))), {k, 0, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Aug 27 2015 *)

Crossrefs

Cf. A000726.

Sequence in context: A336120 A029187 A201863 * A051629 A052120 A179461

Adjacent sequences: A035382 A035383 A035384 * A035386 A035387 A035388

Keyword

nonn

Author

Olivier Gérard

Status

approved