

A035442


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


1



0, 1, 0, 1, 0, 1, 0, 2, 0, 3, 0, 3, 0, 3, 0, 5, 0, 7, 0, 8, 0, 8, 0, 11, 0, 15, 0, 17, 0, 18, 0, 23, 0, 30, 0, 35, 0, 37, 0, 45, 0, 57, 0, 66, 0, 71, 0, 84, 0, 104, 0, 121, 0, 131, 0, 151, 0, 183, 0, 212, 0, 231, 0, 263, 0, 313, 0, 362, 0, 396, 0, 446, 0, 523, 0, 601, 0, 660, 0
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OFFSET

1,8


LINKS

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


FORMULA

If n is even, a(n) ~ 2 * exp(Pi*sqrt(n/6)) * Gamma(5/4) / (6^(3/8) * Pi^(3/4) * n^(7/8)).  Vaclav Kotesovec, Aug 26 2015


MATHEMATICA

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


CROSSREFS

Cf. A035679.
Sequence in context: A243982 A214000 A161123 * A213177 A265017 A349136
Adjacent sequences: A035439 A035440 A035441 * A035443 A035444 A035445


KEYWORD

nonn


AUTHOR

Olivier Gérard


STATUS

approved



