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A349610
Number of solutions to x^2 + y^2 + z^2 <= n^2, where x, y, z are positive odd integers.
4
0, 0, 1, 1, 4, 7, 17, 20, 35, 45, 69, 84, 114, 136, 184, 217, 272, 314, 389, 443, 528, 597, 702, 784, 901, 1018, 1166, 1268, 1442, 1589, 1791, 1926, 2157, 2332, 2584, 2800, 3058, 3293, 3596, 3872, 4194, 4485, 4878, 5184, 5590, 5950, 6388, 6761, 7232
OFFSET
0,5
FORMULA
a(n) = [x^(n^2)] theta_2(x^4)^3 / (8 * (1 - x)).
a(n) = Sum_{k=0..n^2} A008437(k).
a(n) = A053596(n) / 8.
EXAMPLE
a(4) = 4 since there are solutions (1,1,1), (3,1,1), (1,3,1), (1,1,3).
MATHEMATICA
Table[SeriesCoefficient[EllipticTheta[2, 0, x^4]^3/(8 (1 - x)), {x, 0, n^2}], {n, 0, 48}]
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Nov 23 2021
STATUS
approved