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A035467
Number of partitions of n into parts 8k+5 or 8k+7.
1
0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 1, 1, 2, 0, 1, 1, 1, 3, 2, 2, 2, 1, 3, 3, 3, 5, 3, 5, 4, 3, 6, 5, 8, 8, 6, 8, 7, 9, 11, 11, 13, 13, 13, 15, 14, 16, 20, 20, 23, 23, 22, 26, 26, 31, 34, 34, 39, 39, 40, 45, 46, 52, 58, 58, 65, 64, 68, 77, 77, 89, 93, 96, 107, 105, 115, 124, 128, 145
OFFSET
1,15
LINKS
FORMULA
a(n) ~ exp(Pi*sqrt(n/6)) * Gamma(5/8) * Gamma(7/8) / (4 * sqrt(3*Pi) * n). - Vaclav Kotesovec, Aug 27 2015
MATHEMATICA
nmax = 100; Rest[CoefficientList[Series[Product[1/((1 - x^(8k+5))*(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 + 5}~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: A235330 A029394 A357914 * A254045 A024996 A187596
KEYWORD
nonn
STATUS
approved