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A341425
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Number of positive solutions to (x_1)^2 + (x_2)^2 + ... + (x_6)^2 <= n^2.
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7
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7, 48, 331, 1269, 3698, 9382, 20927, 42683, 79844, 142173, 238810, 387615, 603589, 915324, 1345294, 1939221, 2729723, 3783313, 5138567, 6895632, 9108626, 11909496, 15362753, 19642539, 24832744, 31179476, 38757032, 47877886, 58647957, 71447776, 86391220
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OFFSET
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3,1
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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)^6 / (64 * (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, 6):
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MATHEMATICA
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Table[SeriesCoefficient[(EllipticTheta[3, 0, x] - 1)^6/(64 (1 - x)), {x, 0, n^2}], {n, 3, 33}]
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CROSSREFS
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Cf. A000122, A001182, A055405, A055412, A175361, A253663, A302995, A340905, A341401, A341423, A341424, A341426, 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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