A035453 Number of partitions of n into parts 8k+1 or 8k+7.

1, 1, 1, 1, 1, 1, 2, 2, 3, 3, 3, 3, 3, 4, 5, 6, 7, 8, 8, 8, 9, 10, 12, 14, 16, 17, 18, 19, 20, 23, 26, 30, 33, 36, 38, 40, 43, 47, 53, 59, 65, 70, 74, 78, 84, 92, 101, 112, 122, 131, 139, 147, 157, 170, 186, 203, 220, 235, 249, 264, 281, 303, 329, 357, 384, 410, 434, 459

Offset

1,7

Links

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

Formula

a(n) ~ (3+2*sqrt(2))^(1/4) * exp(Pi*sqrt(n/6)) / (4 * 3^(1/4) * n^(3/4)). - Vaclav Kotesovec, Aug 26 2015

Mathematica

nmax = 100; Rest[CoefficientList[Series[Product[1/((1 - x^(8k+1))*(1 - x^(8k+7))), {k, 0, nmax}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, Aug 26 2015 *)
nmax = 60; kmax = nmax/8;
s = Flatten[{Range[0, kmax]*8 + 1}~Join~{Range[0, kmax]*8 + 7}];
Table[Count[IntegerPartitions@n, x_ /; SubsetQ[s, x]], {n, 1, nmax}] (* Robert Price, Aug 03 2020 *)

Crossrefs

Cf. A035684.

Sequence in context: A227002 A343118 A087182 * A272605 A235703 A366664

Adjacent sequences: A035450 A035451 A035452 * A035454 A035455 A035456

Keyword

nonn

Author

Olivier Gérard

Status

approved