A035456 Number of partitions of n into parts 8k+2 or 8k+5.

0, 1, 0, 1, 1, 1, 1, 1, 1, 3, 1, 3, 2, 3, 4, 3, 4, 5, 4, 8, 5, 8, 8, 8, 11, 11, 11, 15, 12, 19, 17, 19, 22, 22, 26, 30, 27, 36, 34, 41, 44, 45, 51, 56, 57, 69, 66, 77, 82, 87, 97, 104, 107, 125, 124, 143, 149, 158, 175, 186, 196, 221, 221, 252, 263, 280, 307, 321, 344, 379

Offset

1,10

Links

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

Formula

a(n) ~ exp(Pi*sqrt(n/6)) * Gamma(5/8) * Gamma(1/4) / (4 * 2^(15/16) * 3^(3/16) * Pi^(9/8) * n^(11/16)). - Vaclav Kotesovec, Aug 26 2015

Mathematica

nmax = 100; Rest[CoefficientList[Series[Product[1/((1 - x^(8k+2))*(1 - x^(8k+5))), {k, 0, nmax}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, Aug 26 2015 *)
nmax = 60; kmax = nmax/8;
s = Flatten[{Range[0, kmax]*8 + 2}~Join~{Range[0, kmax]*8 + 5}];
Table[Count[IntegerPartitions@n, x_ /; SubsetQ[s, x]], {n, 1, nmax}] (* Robert Price, Aug 03 2020 *)

Crossrefs

Cf. A035687.

Sequence in context: A059660 A194003 A339365 * A035664 A095246 A279633

Adjacent sequences: A035453 A035454 A035455 * A035457 A035458 A035459

Keyword

nonn

Author

Olivier Gérard

Status

approved