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Expansion of Product_{k>=0} (1 + x^(4*k+1))*(1 + x^(4*k+2)).
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%I #7 Mar 23 2018 05:01:28

%S 1,1,1,1,0,1,2,2,2,2,2,3,3,3,4,5,6,6,6,7,8,9,10,11,13,14,14,16,18,20,

%T 23,24,27,30,31,34,37,41,46,49,53,58,62,67,73,80,88,94,101,109,117,

%U 127,136,147,161,172,184,198,211,228,245,262,284,304,324,347,370,397,425,454,488

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

%C Number of partitions of n into distinct parts congruent to 1 or 2 mod 4.

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

%F G.f.: Product_{k>=1} (1 + x^A042963(k)).

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

%e a(11) = 3 because we have [10, 1], [9, 2] and [6, 5].

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

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

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

%Y Cf. A035365, A042963, A070048, A108932, A169975, A301504, A301505, A301508.

%K nonn

%O 0,7

%A _Ilya Gutkovskiy_, Mar 22 2018