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%I #6 Nov 26 2019 20:06:29
%S 1,2,4,8,18,40,88,192,420,922,2024,4440,9736,21352,46832,102720,
%T 225298,494144,1083804,2377112,5213736,11435312,25081112,55010496,
%U 120654744,264632554,580419672,1273036832,2792156864,6124049048,13431901808,29460245120,64615275940
%N Expansion of 1 / (1 - 2 * Sum_{k>=1} x^(k^2)).
%F G.f.: 1 / (2 - theta_3(x)), where theta_3() is the Jacobi theta function.
%F a(0) = 1; a(n) = Sum_{k=1..n} A000122(k) * a(n-k).
%t nmax = 32; CoefficientList[Series[1/(1 - 2 Sum[x^(k^2), {k, 1, Floor[Sqrt[nmax]] + 1}]), {x, 0, nmax}], x]
%t nmax = 32; CoefficientList[Series[1/(2 - EllipticTheta[3, 0, x]), {x, 0, nmax}], x]
%t a[0] = 1; a[n_] := a[n] = Sum[SquaresR[1, k] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 32}]
%Y Cf. A000122, A004402, A006456, A025192, A032803, A240944, A279225, A279226, A280542, A320654.
%K nonn
%O 0,2
%A _Ilya Gutkovskiy_, Nov 26 2019
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