A035464 Number of partitions of n into parts 8k+4 or 8k+6.

0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 3, 0, 2, 0, 3, 0, 4, 0, 5, 0, 5, 0, 8, 0, 8, 0, 11, 0, 12, 0, 15, 0, 17, 0, 22, 0, 23, 0, 30, 0, 34, 0, 40, 0, 45, 0, 56, 0, 61, 0, 73, 0, 83, 0, 98, 0, 109, 0, 130, 0, 144, 0, 169, 0, 190, 0, 219, 0, 246, 0, 286, 0, 317, 0, 365, 0, 410, 0, 467, 0

Offset

1,12

Links

Robert Price, Table of n, a(n) for n = 1..1000

Formula

If n is even, a(n) ~ exp(Pi*sqrt(n/6)) * Gamma(3/4) / (2 * 6^(3/8) * Pi^(1/4) * n^(7/8)). - Vaclav Kotesovec, Aug 27 2015

Mathematica

nmax = 100; Rest[CoefficientList[Series[Product[1/((1 - x^(8k+4))*(1 - x^(8k+6))), {k, 0, nmax}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, Aug 27 2015 *)
nmax = 60; kmax = nmax/8;
s = Flatten[{Range[0, kmax]*8 + 4}~Join~{Range[0, kmax]*8 + 6}];
Table[Count[IntegerPartitions@n, x_ /; SubsetQ[s, x]], {n, 1, nmax}] (* Robert Price, Aug 04 2020 *)

Crossrefs

Sequence in context: A241181 A171772 A092735 * A194669 A364570 A302244

Adjacent sequences: A035461 A035462 A035463 * A035465 A035466 A035467

Keyword

nonn

Author

Olivier Gérard

Status

approved