A035445 Number of partitions of n into parts 8k or 8k+5.

0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 2, 0, 1, 2, 0, 2, 0, 1, 4, 0, 2, 3, 1, 5, 0, 2, 7, 1, 5, 5, 2, 9, 1, 5, 12, 2, 10, 8, 5, 17, 2, 10, 20, 5, 19, 13, 10, 29, 5, 20, 32, 10, 34, 20, 20, 49, 10, 36, 50, 20, 59, 32, 37, 78, 20, 64, 77, 37, 97, 50, 66, 124, 37, 107, 117, 67, 157, 79

Offset

1,13

Links

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

Formula

a(n) ~ exp(Pi*sqrt(n/6)) * Gamma(5/8) / (2^(29/16) * 3^(9/16) * Pi^(3/8) * n^(17/16)). - Vaclav Kotesovec, Aug 26 2015

Mathematica

nmax = 100; Rest[CoefficientList[Series[Product[1/((1 - x^(8k+8))*(1 - x^(8k+5))), {k, 0, nmax}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, Aug 26 2015 *)
nmax = 50; kmax = nmax/8;
s = Flatten[{Range[0, kmax]*8}~Join~{Range[0, kmax]*8 + 5}];
Table[Count[IntegerPartitions@n, x_ /; SubsetQ[s, x]], {n, 1, nmax}] (* Robert Price, Aug 03 2020 *)

Crossrefs

Cf. A035676.

Sequence in context: A264394 A283310 A331534 * A053603 A371222 A085794

Adjacent sequences: A035442 A035443 A035444 * A035446 A035447 A035448

Keyword

nonn

Author

Olivier Gérard

Status

approved