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A349609
Number of solutions to x^2 + y^2 <= n^2, where x, y are positive odd integers.
3
0, 0, 1, 1, 3, 4, 8, 8, 13, 15, 20, 22, 28, 31, 39, 43, 52, 54, 64, 69, 79, 83, 96, 102, 112, 121, 135, 140, 154, 162, 179, 185, 203, 212, 228, 238, 255, 265, 281, 296, 316, 326, 349, 359, 382, 394, 416, 429, 451, 469, 494, 508, 532, 547, 573, 587
OFFSET
0,5
FORMULA
a(n) = [x^(n^2)] theta_2(x^4)^2 / (4 * (1 - x)).
a(n) = Sum_{k=0..n^2} A290081(k).
a(n) = A053415(n) / 4.
EXAMPLE
a(4) = 3 since there are solutions (1,1), (3,1), (1,3).
MATHEMATICA
Table[SeriesCoefficient[EllipticTheta[2, 0, x^4]^2/(4 (1 - x)), {x, 0, n^2}], {n, 0, 55}]
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Nov 23 2021
STATUS
approved