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Expansion of (x/(4 * (1-x))) * d/dx(theta_3(x)^2).
1

%I #14 Jul 11 2024 08:38:19

%S 0,1,3,3,7,17,17,17,25,34,54,54,54,80,80,80,96,130,148,148,188,188,

%T 188,188,188,263,315,315,315,373,373,373,405,405,473,473,509,583,583,

%U 583,663,745,745,745,745,835,835,835,835,884,1034,1034,1138,1244,1244,1244,1244,1244,1360,1360

%N Expansion of (x/(4 * (1-x))) * d/dx(theta_3(x)^2).

%F a(n) = 1/4 * Sum_{i,j in Z and i^2 + j^2 <= n} i^2 + j^2.

%F G.f.: (1/(1-x)) * Sum_{k>=1} k * x^k * (1-x^(2*k)) / (1+x^(2*k))^2.

%o (PARI) my(N=60, x='x+O('x^N)); concat(0, Vec(sum(k=1, N, k*x^k*(1-x^(2*k))/(1+x^(2*k))^2)/(1-x)))

%Y Partial sums of A111938.

%Y Cf. A014203, A374535.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Jul 11 2024