A219607 Number of partitions of n into distinct parts 5*k+2 or 5*k+3.
1, 0, 1, 1, 0, 1, 0, 1, 1, 1, 2, 1, 2, 2, 1, 3, 1, 3, 3, 2, 5, 3, 5, 5, 4, 7, 4, 7, 7, 6, 11, 7, 11, 11, 9, 15, 10, 15, 16, 14, 22, 16, 23, 23, 20, 30, 22, 31, 32, 29, 42, 33, 44, 45, 41, 56, 45, 59, 61, 57, 78, 64, 82, 84, 78, 103, 86, 108, 112, 107, 138
Offset: 0
Keywords
Examples
a(10) = #{8+2, 7+3} = 2;
a(11) = #{8+3} = 1;
a(12) = #{12, 7+3+2} = 2;
a(13) = #{13, 8+3+2} = 2;
a(14) = #{12+2} = 1;
a(15) = #{13+2, 12+3, 8+7} = 3;
a(16) = #{13+3} = 1;
a(17) = #{17, 12+3+2, 8+7+2} = 3;
a(18) = #{18, 13+3+2, 8+7+3} = 3;
a(19) = #{17+2, 12+7} = 2;
a(20) = #{18+2, 17+3, 13+7, 12+8, 8+7+3+2} = 5.
Links
- Seiichi Manyama, Table of n, a(n) for n = 0..1000 (terms 0..250 from Reinhard Zumkeller)
Programs
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Haskell
a219607 = p a047221_list where p _ 0 = 1 p (k:ks) m = if m < k then 0 else p ks (m - k) + p ks m
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Mathematica
nmax = 100; CoefficientList[Series[Product[(1 + x^(5*k - 2))*(1 + x^(5*k - 3)), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Jan 18 2017 *)
Formula
a(n) ~ exp(sqrt(2*n/15)*Pi) / (2*30^(1/4)*n^(3/4)) * (1 - (3*sqrt(15/2)/(8*Pi) + 11*Pi/(60*sqrt(30))) / sqrt(n)). - Vaclav Kotesovec, Jan 18 2017, extended Jan 24 2017
Comments