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A081055 Number of partitions of 2n in which no parts are multiples of 4.

%I A081055 #15 Jul 28 2020 17:17:45
%S A081055 1,2,4,9,16,29,50,82,132,208,320,484,722,1060,1539,2210,3138,4416,
%T A081055 6163,8528,11716,15986,21666,29190,39104,52098,69060,91106,119634,
%U A081055 156416,203664,264128,341256,439321,563600,720648,918530,1167154,1478720
%N A081055 Number of partitions of 2n in which no parts are multiples of 4.
%C A081055 Euler transform of period 16 sequence [2,1,3,1,3,0,2,0,2,0,3,1,3,1,2,0,...].
%H A081055 Seiichi Manyama, <a href="/A081055/b081055.txt">Table of n, a(n) for n = 0..10000</a>
%F A081055 G.f.: (sum_{n>=0} x^A074378(n))/(sum_n (-x)^n^2).
%F A081055 a(n) = A001935(2n).
%F A081055 a(n) ~ exp(Pi*sqrt(n)) / (2^(7/2) * n^(3/4)). - _Vaclav Kotesovec_, Nov 15 2017
%t A081055 Table[Count[IntegerPartitions[2n], x_ /; ! MemberQ [Mod[x, 4], 0, 2] ], {n, 0, 38}] (* _Robert Price_, Jul 28 2020 *)
%o A081055 (PARI) a(n)=local(X); if(n<0,0,X=x+x*O(x^(2*n)); polcoeff(eta(X^4)/eta(X),2*n))
%Y A081055 Cf. A001935, A074378, A081056.
%K A081055 nonn,easy
%O A081055 0,2
%A A081055 _Michael Somos_, Mar 03 2003