A035372 Number of partitions of n into parts 5k+1 or 5k+3.
1, 1, 2, 2, 2, 4, 4, 5, 7, 7, 9, 12, 13, 16, 19, 22, 26, 31, 36, 41, 48, 56, 63, 75, 85, 96, 112, 126, 143, 165, 184, 210, 238, 267, 302, 340, 381, 428, 480, 538, 599, 672, 748, 832, 930, 1031, 1144, 1275, 1408, 1562, 1730, 1910, 2111, 2332, 2571, 2834, 3121
Offset: 1
Keywords
Programs
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Mathematica
nmax = 100; Rest[CoefficientList[Series[Product[1/((1 - x^(5k+1))*(1 - x^(5k+3))), {k, 0, nmax}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, Aug 27 2015 *)
Formula
a(n) ~ exp(2*Pi*sqrt(n/15)) * Gamma(1/5) * Gamma(3/5) / (4 * 3^(3/20) * 5^(7/20) * Pi^(6/5) * n^(13/20)). - Vaclav Kotesovec, Aug 27 2015