A035446 Number of partitions of n into parts 8k or 8k+6.

0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 2, 0, 2, 0, 1, 0, 2, 0, 4, 0, 4, 0, 2, 0, 5, 0, 8, 0, 7, 0, 5, 0, 10, 0, 14, 0, 12, 0, 11, 0, 19, 0, 24, 0, 22, 0, 21, 0, 33, 0, 41, 0, 37, 0, 38, 0, 58, 0, 67, 0, 62, 0, 68, 0, 95, 0, 108, 0, 103, 0, 114, 0, 155, 0, 172, 0, 166, 0, 188, 0, 246, 0

Offset

1,14

Links

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

Formula

If n is even, a(n) ~ exp(Pi*sqrt(n/6)) * Gamma(3/4) / (6^(5/8) * Pi^(1/4) * n^(9/8)). - Vaclav Kotesovec, Aug 26 2015

Mathematica

nmax = 100; Rest[CoefficientList[Series[Product[1/((1 - x^(8k+8))*(1 - x^(8k+6))), {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 + 6}];
Table[Count[IntegerPartitions@n, x_ /; SubsetQ[s, x]], {n, 1, nmax}] (* Robert Price, Aug 03 2020 *)

Crossrefs

Sequence in context: A352567 A088700 A287121 * A126211 A095414 A339012

Adjacent sequences: A035443 A035444 A035445 * A035447 A035448 A035449

Keyword

nonn

Author

Olivier Gérard

Status

approved