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A035448
Number of partitions of n into parts 8k+1 or 8k+2.
1
1, 2, 2, 3, 3, 4, 4, 5, 6, 8, 9, 11, 12, 14, 15, 17, 19, 23, 26, 31, 34, 39, 42, 47, 51, 58, 65, 74, 82, 92, 100, 110, 119, 132, 145, 163, 179, 199, 216, 237, 255, 279, 303, 334, 365, 401, 435, 473, 509, 552, 596, 650, 705, 770, 832, 902, 968, 1044, 1121, 1213
OFFSET
1,2
LINKS
FORMULA
a(n) ~ exp(Pi*sqrt(n/6)) * Gamma(1/4) * Gamma(1/8) * 3^(1/16) / (8 * 2^(11/16) * Pi^(13/8) * n^(7/16)). - Vaclav Kotesovec, Aug 26 2015
MATHEMATICA
nmax = 100; Rest[CoefficientList[Series[Product[1/((1 - x^(8k+1))*(1 - x^(8k+2))), {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 + 2}];
Table[Count[IntegerPartitions@n, x_ /; SubsetQ[s, x]], {n, 1, nmax}] (* Robert Price, Aug 03 2020 *)
CROSSREFS
Cf. A035679.
Sequence in context: A029072 A279766 A029027 * A060969 A367694 A358151
KEYWORD
nonn
STATUS
approved