A035466 Number of partitions of n into parts 8k+5 or 8k+6.

0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 4, 4, 4, 4, 5, 5, 6, 6, 7, 8, 8, 8, 9, 10, 12, 12, 14, 14, 15, 16, 17, 19, 22, 22, 24, 25, 27, 29, 32, 34, 38, 39, 42, 44, 48, 51, 55, 59, 64, 67, 72, 75, 81, 87, 94, 99, 107, 111, 119, 126, 135, 144, 154

Offset

1,18

Links

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

Formula

a(n) ~ exp(Pi*sqrt(n/6)) * Gamma(5/8) * Gamma(3/4) / (4 * 2^(3/16) * 3^(7/16) * Pi^(5/8) * n^(15/16)). - Vaclav Kotesovec, Aug 27 2015

Mathematica

nmax = 100; Rest[CoefficientList[Series[Product[1/((1 - x^(8k+5))*(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 + 5}~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: A236678 A029378 A053278 * A122521 A086394 A029226

Adjacent sequences: A035463 A035464 A035465 * A035467 A035468 A035469

Keyword

nonn

Author

Olivier Gérard

Status

approved