%I #7 Mar 24 2018 19:06:07
%S 1,1,1,1,0,0,1,2,2,2,1,1,2,3,3,2,2,3,5,6,5,4,4,6,8,8,7,7,9,12,13,11,
%T 10,12,16,19,19,17,18,23,27,27,25,25,30,37,40,38,37,42,50,55,54,52,57,
%U 68,77,78,75,78,90,102,106,104,106,120,138,146,144,145,158
%N Expansion of Product_{k>=0} (1 + x^(5*k+1))*(1 + x^(5*k+2)).
%C Number of partitions of n into distinct parts congruent to 1 or 2 mod 5.
%H <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F G.f.: Product_{k>=1} (1 + x^A047216(k)).
%F a(n) ~ exp(Pi*sqrt(2*n/15)) / (2^(17/20) * 15^(1/4) * n^(3/4)). - _Vaclav Kotesovec_, Mar 24 2018
%e a(13) = 3 because we have [12, 1], [11, 2] and [7, 6].
%t nmax = 70; CoefficientList[Series[Product[(1 + x^(5 k + 1)) (1 + x^(5 k + 2)), {k, 0, nmax}], {x, 0, nmax}], x]
%t nmax = 70; CoefficientList[Series[QPochhammer[-x, x^5] QPochhammer[-x^2, x^5], {x, 0, nmax}], x]
%t nmax = 70; CoefficientList[Series[Product[(1 + Boole[MemberQ[{1, 2}, Mod[k, 5]]] x^k), {k, 1, nmax}], {x, 0, nmax}], x]
%Y Cf. A035371, A047216, A107234, A107235, A203776, A219607, A280454, A281272, A301563, A301564, A301565, A301567, A301568, A301569, A301570.
%K nonn
%O 0,8
%A _Ilya Gutkovskiy_, Mar 23 2018
|