cp's OEIS Frontend

A363903 Expansion of Sum_{k>0} x^k / (1 - x^(4*k))^2.

%I A363903 #17 Jun 29 2023 08:58:08
%S A363903 1,1,1,1,3,1,1,1,4,3,1,1,5,1,3,1,6,4,1,3,7,1,1,1,10,5,4,1,9,3,1,1,10,
%T A363903 6,3,4,11,1,5,3,12,7,1,1,18,1,1,1,14,10,6,5,15,4,3,1,16,9,1,3,17,1,10,
%U A363903 1,24,10,1,6,19,3,1,4,20,11,10,1,21,5,1,3,25,12,1,7,30,1,9,1,24,18,5,1,25,1,3,1
%N A363903 Expansion of Sum_{k>0} x^k / (1 - x^(4*k))^2.
%H A363903 Seiichi Manyama, <a href="/A363903/b363903.txt">Table of n, a(n) for n = 1..10000</a>
%F A363903 a(n) = (1/4) * Sum_{d|n, d==1 mod 4} (d+3) = (3 * A001826(n) + A050449(n))/4.
%F A363903 G.f.: Sum_{k>0} k * x^(4*k-3) / (1 - x^(4*k-3)).
%t A363903 a[n_] := DivisorSum[n, # + 3 &, Mod[#, 4] == 1 &]/4; Array[a, 100] (* _Amiram Eldar_, Jun 27 2023 *)
%o A363903 (PARI) a(n) = sumdiv(n, d, (d%4==1)*(d+3))/4;
%Y A363903 Cf. A363901, A363925.
%Y A363903 Cf. A001826, A050449.
%K A363903 nonn
%O A363903 1,5
%A A363903 _Seiichi Manyama_, Jun 27 2023