A301505 - OEIS

%I #7 Mar 23 2018 05:01:06

%S 1,0,0,1,1,0,0,2,1,0,1,3,2,0,2,5,2,0,4,7,3,1,7,10,4,2,11,14,5,4,17,19,

%T 6,8,25,25,9,13,36,33,12,21,50,43,16,33,69,55,23,49,93,70,32,71,124,

%U 89,45,102,163,112,64,142,212,141,89,195,273,177,123,265,349

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

%C Number of partitions of n into distinct parts congruent to 0 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^A014601(k)).

%F a(n) ~ exp(Pi*sqrt(n/6)) / (2^(5/2)*3^(1/4)*n^(3/4)). - _Vaclav Kotesovec_, Mar 23 2018

%e a(11) = 3 because we have [11], [8, 3] and [7, 4].

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

%t nmax = 70; CoefficientList[Series[x QPochhammer[-1, x^4] QPochhammer[-x^(-1), x^4]/(2 (1 + x)), {x, 0, nmax}], x]

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

%Y Cf. A014601, A035364, A035457, A131795, A147599, A301504, A301507, A301508.

%K nonn

%O 0,8

%A _Ilya Gutkovskiy_, Mar 22 2018