%I #7 Mar 23 2018 05:00:37

%S 1,0,1,1,0,1,1,1,1,2,2,2,2,3,2,3,4,4,5,5,6,7,6,8,9,9,11,12,13,14,15,

%T 17,19,20,23,25,27,29,31,35,37,40,46,48,52,57,60,66,71,76,85,90,97,

%U 105,112,121,129,140,152,161,174,187,198,214,228,245,265,280,302,323,342

%N Expansion of Product_{k>=0} (1 + x^(4*k+2))*(1 + x^(4*k+3)).

%C Number of partitions of n into distinct parts congruent to 2 or 3 mod 4.

%H <a href="/index/Par#part">Index entries for sequences related to partitions</a>

%F G.f.: Product_{k>=1} (1 + x^A042964(k)).

%F a(n) ~ exp(Pi*sqrt(n/6)) / (4*3^(1/4)*n^(3/4)). - _Vaclav Kotesovec_, Mar 23 2018

%e a(13) = 3 because we have [11, 2], [10, 3] and [7, 6].

%t nmax = 70; CoefficientList[Series[Product[(1 + x^(4 k + 2)) (1 + x^(4 k + 3)), {k, 0, nmax}], {x, 0, nmax}], x]

%t nmax = 70; CoefficientList[Series[QPochhammer[-x^2, x^4] QPochhammer[-x^3, x^4], {x, 0, nmax}], x]

%t nmax = 70; CoefficientList[Series[Product[(1 + Boole[MemberQ[{2, 3}, Mod[k, 4]]] x^k), {k, 1, nmax}], {x, 0, nmax}], x]

%Y Cf. A035366, A042964, A070048, A131795, A147599, A301504, A301505, A301507.

%K nonn

%O 0,10

%A _Ilya Gutkovskiy_, Mar 22 2018