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A081056 Number of partitions of 2n+1 in which no parts are multiples of 4.

%I A081056 #16 Sep 11 2019 09:51:11
%S A081056 1,3,6,12,22,38,64,105,166,258,395,592,876,1280,1846,2636,3728,5222,
%T A081056 7256,10006,13696,18624,25169,33808,45164,60022,79366,104457,136870,
%U A081056 178572,232044,300368,387366,497804,637568,813910,1035792,1314214
%N A081056 Number of partitions of 2n+1 in which no parts are multiples of 4.
%C A081056 Euler transform of period 16 sequence [3,0,2,1,2,1,3,0,3,1,2,1,2,0,3,0,...].
%H A081056 Seiichi Manyama, <a href="/A081056/b081056.txt">Table of n, a(n) for n = 0..10000</a>
%F A081056 G.f.: (sum_{n>=0} x^A074377(n))/(sum_n (-x)^n^2).
%F A081056 a(n) = A001935(2n+1).
%F A081056 a(n) ~ exp(Pi*sqrt(n)) / (2^(7/2) * n^(3/4)). - _Vaclav Kotesovec_, Nov 15 2017
%t A081056 Table[Count[IntegerPartitions[2n+1],_?(Total[Boole[Divisible[#,4]]]==0&)],{n,0,40}] (* _Harvey P. Dale_, Sep 11 2019 *)
%o A081056 (PARI) a(n)=local(X); if(n<0,0,X=x+x^2*O(x^(2*n)); polcoeff(eta(X^4)/eta(X),2*n+1))
%Y A081056 Cf. A001935, A074377, A081055.
%K A081056 nonn,easy
%O A081056 0,2
%A A081056 _Michael Somos_, Mar 03 2003