A035465 Number of partitions of n into parts 8k+4 or 8k+7.

0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 2, 0, 1, 2, 2, 0, 1, 3, 3, 1, 2, 4, 4, 1, 3, 6, 6, 2, 5, 8, 7, 3, 7, 12, 10, 5, 10, 15, 13, 7, 15, 21, 17, 11, 20, 27, 22, 16, 28, 36, 29, 22, 37, 46, 38, 31, 50, 60, 50, 42, 65, 77, 64, 57, 86, 99, 82, 76, 111, 125, 106, 101, 144, 159, 135, 132

Offset

1,12

Links

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

Formula

a(n) ~ exp(Pi*sqrt(n/6)) * Gamma(7/8) / (4 * 2^(3/16) * 3^(7/16) * Pi^(1/8) * n^(15/16)). - Vaclav Kotesovec, Aug 27 2015

Mathematica

nmax = 100; Rest[CoefficientList[Series[Product[1/((1 - x^(8k+4))*(1 - x^(8k+7))), {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 + 7}];
Table[Count[IntegerPartitions@n, x_ /; SubsetQ[s, x]], {n, 1, nmax}] (* Robert Price, Aug 04 2020 *)

Crossrefs

Sequence in context: A133121 A091602 A336695 * A096144 A118401 A354786

Adjacent sequences: A035462 A035463 A035464 * A035466 A035467 A035468

Keyword

nonn

Author

Olivier Gérard

Status

approved