A374534 Expansion of (x/(4 * (1-x))) * d/dx(theta_3(x)^2).
0, 1, 3, 3, 7, 17, 17, 17, 25, 34, 54, 54, 54, 80, 80, 80, 96, 130, 148, 148, 188, 188, 188, 188, 188, 263, 315, 315, 315, 373, 373, 373, 405, 405, 473, 473, 509, 583, 583, 583, 663, 745, 745, 745, 745, 835, 835, 835, 835, 884, 1034, 1034, 1138, 1244, 1244, 1244, 1244, 1244, 1360, 1360
Offset: 0
Keywords
Programs
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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)))
Formula
a(n) = 1/4 * Sum_{i,j in Z and i^2 + j^2 <= n} i^2 + j^2.
G.f.: (1/(1-x)) * Sum_{k>=1} k * x^k * (1-x^(2*k)) / (1+x^(2*k))^2.