A035455 Number of partitions of n into parts 8k+2 or 8k+4.

0, 1, 0, 2, 0, 2, 0, 3, 0, 4, 0, 6, 0, 7, 0, 9, 0, 11, 0, 15, 0, 18, 0, 23, 0, 27, 0, 34, 0, 41, 0, 50, 0, 59, 0, 72, 0, 85, 0, 103, 0, 120, 0, 143, 0, 167, 0, 198, 0, 230, 0, 270, 0, 313, 0, 366, 0, 422, 0, 491, 0, 564, 0, 653, 0, 748, 0, 861, 0, 984, 0, 1130, 0, 1287, 0, 1471, 0

Offset

1,4

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(1/4) / (4 * 6^(1/8) * Pi^(3/4) * n^(5/8)). - Vaclav Kotesovec, Aug 26 2015

Mathematica

nmax = 100; Rest[CoefficientList[Series[Product[1/((1 - x^(8k+2))*(1 - x^(8k+4))), {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 + 4}];
Table[Count[IntegerPartitions@n, x_ /; SubsetQ[s, x]], {n, 1, nmax}] (* Robert Price, Aug 03 2020 *)

Crossrefs

Cf. A035686.

Sequence in context: A165685 A035457 A005868 * A029191 A094098 A326844

Adjacent sequences: A035452 A035453 A035454 * A035456 A035457 A035458

Keyword

nonn

Author

Olivier Gérard

Status

approved