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 A302995 a(n) = [x^(n^2)] (theta_3(x) - 1)^n/(2^n*(1 - x)), where theta_3() is the Jacobi theta function. 8
 1, 1, 1, 7, 32, 177, 1269, 9263, 74452, 652710, 6078048, 60447082, 631870024, 6915613084, 79113376037, 941759419159, 11630647314564, 148799595377384, 1966441829785081, 26793749867965515, 375812005722920406, 5416574818546042067, 80123280319100908258, 1214860029446181979357 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS a(n) = number of positive solutions to (x_1)^2 + (x_2)^2 + ... + (x_n)^2 <= n^2. LINKS Eric Weisstein's World of Mathematics, Jacobi Theta Functions MATHEMATICA Table[SeriesCoefficient[(EllipticTheta[3, 0, x] - 1)^n/(2^n (1 - x)), {x, 0, n^2}], {n, 0, 23}] Join[{1}, Table[SeriesCoefficient[1/(1 - x) Sum[x^k^2, {k, 1, n}]^n, {x, 0, n^2}], {n, 23}]] CROSSREFS Cf. A000122, A001182, A253663, A298330, A302861, A302863. Sequence in context: A188179 A050148 A188208 * A188331 A177766 A240390 Adjacent sequences:  A302992 A302993 A302994 * A302996 A302997 A302998 KEYWORD nonn AUTHOR Ilya Gutkovskiy, Apr 17 2018 STATUS approved

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Last modified September 28 06:17 EDT 2021. Contains 347703 sequences. (Running on oeis4.)