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%I #16 Aug 23 2023 17:00:32
%S 0,0,1,1,4,7,17,20,35,45,69,84,114,136,184,217,272,314,389,443,528,
%T 597,702,784,901,1018,1166,1268,1442,1589,1791,1926,2157,2332,2584,
%U 2800,3058,3293,3596,3872,4194,4485,4878,5184,5590,5950,6388,6761,7232
%N Number of solutions to x^2 + y^2 + z^2 <= n^2, where x, y, z are positive odd integers.
%H David A. Corneth, <a href="/A349610/b349610.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 a(n) = [x^(n^2)] theta_2(x^4)^3 / (8 * (1 - x)).
%F a(n) = Sum_{k=0..n^2} A008437(k).
%F a(n) = A053596(n) / 8.
%e a(4) = 4 since there are solutions (1,1,1), (3,1,1), (1,3,1), (1,1,3).
%t Table[SeriesCoefficient[EllipticTheta[2, 0, x^4]^3/(8 (1 - x)), {x, 0, n^2}], {n, 0, 48}]
%Y Cf. A000604, A000605, A008437, A053596, A085121, A253663, A349609, A349611.
%K nonn
%O 0,5
%A _Ilya Gutkovskiy_, Nov 23 2021