A302995 a(n) = [x^(n^2)] (theta_3(x) - 1)^n/(2^n*(1 - x)), where theta_3() is the Jacobi theta function.

1, 1, 1, 7, 32, 177, 1269, 9263, 74452, 652710, 6078048, 60447082, 631870024, 6915613084, 79113376037, 941759419159, 11630647314564, 148799595377384, 1966441829785081, 26793749867965515, 375812005722920406, 5416574818546042067, 80123280319100908258, 1214860029446181979357

Offset

0,4

Comments

a(n) = number of positive solutions to (x_1)^2 + (x_2)^2 + ... + (x_n)^2 <= n^2.

Links

Table of n, a(n) for n=0..23.

Eric Weisstein's World of Mathematics, Jacobi Theta Functions

Index entries for sequences related to sums of squares

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