A035459 Number of partitions of n into parts 8k+3 or 8k+4.

0, 0, 1, 1, 0, 1, 1, 1, 1, 1, 2, 3, 1, 2, 4, 3, 2, 4, 5, 5, 4, 6, 8, 8, 6, 9, 12, 11, 9, 14, 17, 15, 15, 20, 23, 23, 21, 28, 34, 31, 30, 41, 45, 43, 44, 55, 62, 60, 60, 76, 84, 80, 83, 103, 112, 108, 114, 138, 148, 146, 153, 182, 197, 192, 203, 243, 256, 252, 272, 315, 333

Offset

1,11

Links

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

Formula

a(n) ~ exp(Pi*sqrt(n/6)) * Gamma(3/8) / (4 * 2^(15/16) * 3^(3/16) * Pi^(5/8) * n^(11/16)). - Vaclav Kotesovec, Aug 26 2015

Mathematica

nmax = 100; Rest[CoefficientList[Series[Product[1/((1 - x^(8k+3))*(1 - x^(8k+4))), {k, 0, nmax}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, Aug 26 2015 *)
nmax = 60; kmax = nmax/8;
s = Flatten[{Range[0, kmax]*8 + 3}~Join~{Range[0, kmax]*8 + 4}];
Table[Count[IntegerPartitions@n, x_ /; SubsetQ[s, x]], {n, 1, nmax}] (* Robert Price, Aug 04 2020 *)

Crossrefs

Cf. A035690.

Sequence in context: A256990 A071503 A029271 * A048232 A163256 A199263

Adjacent sequences: A035456 A035457 A035458 * A035460 A035461 A035462

Keyword

nonn

Author

Olivier Gérard

Status

approved