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A349609
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Number of solutions to x^2 + y^2 <= n^2, where x, y are positive odd integers.
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3
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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
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OFFSET
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0,5
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LINKS
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FORMULA
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a(n) = [x^(n^2)] theta_2(x^4)^2 / (4 * (1 - x)).
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EXAMPLE
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a(4) = 3 since there are solutions (1,1), (3,1), (1,3).
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MATHEMATICA
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Table[SeriesCoefficient[EllipticTheta[2, 0, x^4]^2/(4 (1 - x)), {x, 0, n^2}], {n, 0, 55}]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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