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%I #8 Mar 24 2018 19:06:44
%S 1,1,0,1,1,0,1,1,1,2,1,2,2,1,3,2,2,4,3,4,4,4,6,4,6,7,5,9,8,8,11,9,12,
%T 12,12,16,13,17,19,17,23,21,24,27,24,32,30,32,40,35,43,45,44,53,50,59,
%U 62,61,75,70,78,87,83,99,97,105,118,112,133,134,138,159,153
%N Expansion of Product_{k>=0} (1 + x^(5*k+1))*(1 + x^(5*k+3)).
%C Number of partitions of n into distinct parts congruent to 1 or 3 mod 5.
%H <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F G.f.: Product_{k>=1} (1 + x^A047219(k)).
%F a(n) ~ exp(Pi*sqrt(2*n/15)) / (2^(21/20) * 15^(1/4) * n^(3/4)). - _Vaclav Kotesovec_, Mar 24 2018
%e a(14) = 3 because we have [13, 1], [11, 3] and [8, 6].
%t nmax = 72; CoefficientList[Series[Product[(1 + x^(5 k + 1)) (1 + x^(5 k + 3)), {k, 0, nmax}], {x, 0, nmax}], x]
%t nmax = 72; CoefficientList[Series[QPochhammer[-x, x^5] QPochhammer[-x^3, x^5], {x, 0, nmax}], x]
%t nmax = 72; CoefficientList[Series[Product[(1 + Boole[MemberQ[{1, 3}, Mod[k, 5]]] x^k), {k, 1, nmax}], {x, 0, nmax}], x]
%Y Cf. A035372, A047219, A107234, A107236, A203776, A219607, A280454, A281271, A301562, A301564, A301565, A301567, A301568, A301569, A301570.
%K nonn
%O 0,10
%A _Ilya Gutkovskiy_, Mar 23 2018
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