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A341426
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Number of positive solutions to (x_1)^2 + (x_2)^2 + ... + (x_7)^2 <= n^2.
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7
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1, 71, 491, 2522, 9263, 27723, 71480, 163908, 345657, 679802, 1252185, 2203724, 3715206, 6041979, 9510283, 14591324, 21788606, 31894205, 45741815, 64467383, 89363919, 122254946, 164721244, 219526449, 289133792, 377013829, 486522424, 622759365
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OFFSET
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3,2
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LINKS
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FORMULA
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a(n) is the coefficient of x^(n^2) in expansion of (theta_3(x) - 1)^7 / (128 * (1 - x)).
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MAPLE
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b:= proc(n, k) option remember; `if`(k=0, 1, `if`(n=0, 0,
add((s->`if`(s>n, 0, b(n-s, k-1)))(j^2), j=1..isqrt(n))))
end:
a:= n-> b(n^2, 7):
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MATHEMATICA
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Table[SeriesCoefficient[(EllipticTheta[3, 0, x] - 1)^7/(128 (1 - x)), {x, 0, n^2}], {n, 3, 30}]
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CROSSREFS
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Cf. A000122, A001182, A055406, A055413, A253663, A302995, A340906, A341396, A341402, A341423, A341424, A341425, A341427, A341428, A341429.
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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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