|
%I #7 Mar 24 2018 19:07:56
%S 1,0,0,1,1,0,0,1,1,1,0,1,2,2,1,1,2,3,2,1,2,4,4,3,3,4,6,6,4,4,7,9,7,6,
%T 8,11,12,10,9,12,16,16,14,14,19,23,22,19,21,27,31,29,26,31,40,42,38,
%U 38,45,53,55,51,52,63,73,73,69,73,87,97,95,91,100,118,128
%N Expansion of Product_{k>=0} (1 + x^(5*k+3))*(1 + x^(5*k+4)).
%C Number of partitions of n into distinct parts congruent to 3 or 4 mod 5.
%H <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F G.f.: Product_{k>=1} (1 + x^A047204(k)).
%F a(n) ~ exp(Pi*sqrt(2*n/15)) / (2^(33/20) * 15^(1/4) * n^(3/4)). - _Vaclav Kotesovec_, Mar 24 2018
%e a(17) = 3 because we have [14, 3], [13, 4] and [9, 8].
%t nmax = 74; CoefficientList[Series[Product[(1 + x^(5 k + 3)) (1 + x^(5 k + 4)), {k, 0, nmax}], {x, 0, nmax}], x]
%t nmax = 74; CoefficientList[Series[QPochhammer[-x^3, x^5] QPochhammer[-x^4, x^5], {x, 0, nmax}], x]
%t nmax = 74; CoefficientList[Series[Product[(1 + Boole[MemberQ[{3, 4}, Mod[k, 5]]] x^k), {k, 1, nmax}], {x, 0, nmax}], x]
%Y Cf. A035374, A047204, A107236, A107237, A203776, A219607, A281243, A281271, A301562, A301563, A301564, A301567, A301568, A301569, A301570.
%K nonn
%O 0,13
%A _Ilya Gutkovskiy_, Mar 23 2018
|
