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%I #7 Feb 10 2021 19:31:10
%S 1,6,16,26,36,57,87,107,122,157,207,247,277,322,392,452,482,537,637,
%T 717,773,863,973,1053,1113,1203,1343,1473,1553,1668,1858,1998,2053,
%U 2173,2373,2543,2673,2818,3018,3218,3338,3483,3753,3973,4113,4344,4634,4834,4944,5139,5449
%N Number of nonnegative solutions to (x_1)^2 + (x_2)^2 + ... + (x_5)^2 <= n.
%C Partial sums of A038671.
%H <a href="/index/Su#ssq">Index entries for sequences related to sums of squares</a>
%F G.f.: (1 + theta_3(x))^5 / (32 * (1 - x)).
%F a(n^2) = A055404(n).
%p b:= proc(n, k) option remember; `if`(n=0, 1, `if`(n<0 or k<1, 0,
%p b(n, k-1)+add(b(n-j^2, k-1), j=1..isqrt(n))))
%p end:
%p a:= proc(n) option remember; b(n, 5)+`if`(n>0, a(n-1), 0) end:
%p seq(a(n), n=0..50); # _Alois P. Heinz_, Feb 10 2021
%t nmax = 50; CoefficientList[Series[(1 + EllipticTheta[3, 0, x])^5/(32 (1 - x)), {x, 0, nmax}], x]
%Y Cf. A000122, A000606, A003059, A038671, A055404, A055411, A175360, A224212, A224213, A302862, A341401, A341402.
%K nonn
%O 0,2
%A _Ilya Gutkovskiy_, Feb 10 2021
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