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%I #4 Jan 16 2017 14:19:07
%S 0,0,0,0,0,0,0,0,1,0,0,0,0,2,0,0,0,0,1,0,2,0,0,0,0,2,0,0,0,2,0,0,1,0,
%T 2,0,0,0,0,0,2,2,0,0,0,2,0,0,0,0,1,0,2,2,0,0,0,0,2,0,0,2,0,0,0,2,0,0,
%U 2,0,0,0,1,2,2,0,0,0,0,0,2,0,0,0,0,4,0,0,0,2,2,0,0,0,0,0,0,2,1,0,2,0,0,0,2
%N Expansion of (Sum_{k>=2} x^(k^2))^2.
%C Number of ways to write n as an ordered sum of 2 squares > 1.
%H <a href="/index/Su#ssq">Index entries for sequences related to sums of squares</a>
%F G.f.: (Sum_{k>=2} x^(k^2))^2.
%F G.f.: (1/4)*(1 + 2*x - theta_3(0,x))^2, where theta_3 is the 3rd Jacobi theta function.
%e G.f. = x^8 + 2*x^13 + x^18 + 2*x^20 + 2*x^25 + 2*x^29 + x^32 + 2*x^34 + 2*x^40 + ...
%e a(13) = 2 because we have [9, 4] and [4, 9].
%t nmax = 105; CoefficientList[Series[Sum[x^k^2, {k, 2, nmax}]^2, {x, 0, nmax}], x]
%t CoefficientList[Series[(1 + 2 x - EllipticTheta[3, 0, x])^2/4, {x, 0, 105}], x]
%Y Cf. A000290, A000925, A004018, A006456, A063725, A078134, A085989, A280542.
%K nonn
%O 0,14
%A _Ilya Gutkovskiy_, Jan 16 2017