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%I #16 Aug 26 2019 10:08:02
%S 1,6,15,20,21,36,61,60,45,72,120,120,95,120,186,200,141,150,270,300,
%T 216,252,375,360,271,306,450,500,390,396,626,660,405,420,735,780,582,
%U 600,825,920,720,606,960,1140,825
%N Number of nonnegative solutions of x1^2 + x2^2 + ... + x6^2 = n.
%H T. D. Noe, <a href="/A045848/b045848.txt">Table of n, a(n) for n = 0..10000</a>
%H <a href="/index/Su#ssq">Index entries for sequences related to sums of squares</a>
%F Coefficient of q^n in (1 + q + q^4 + q^9 + q^16 + q^25 + q^36 + q^49 + q^64 + ...)^6.
%F G.f.: (1 + theta_3(q))^6/64, where theta_3() is the Jacobi theta function. - _Ilya Gutkovskiy_, Aug 08 2018
%t (1 + EllipticTheta[3, 0, q])^6/64 + O[q]^45 // CoefficientList[#, q]& (* _Jean-François Alcover_, Aug 26 2019 *)
%o (PARI) seq(n)=Vec((sum(k=0, sqrtint(n), x^(k^2)) + O(x*x^n))^6) \\ _Andrew Howroyd_, Aug 08 2018
%K nonn
%O 0,2
%A _N. J. A. Sloane_
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