A302860 - OEIS

A302860

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

1, 3, 9, 27, 89, 333, 1341, 5449, 21697, 84663, 327829, 1275739, 5020457, 19964623, 79883141, 320317827, 1284656385, 5152761033, 20686311261, 83182322509, 335110196569, 1352277390001, 5463873556381, 22097867887045, 89441286136465, 362277846495883, 1468465431530457

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OFFSET

0,2

COMMENTS

a(n) = number of integer lattice points inside the n-dimensional hypersphere of radius sqrt(n).

LINKS

Table of n, a(n) for n=0..26.

Eric Weisstein's World of Mathematics, Jacobi Theta Functions

Index entries for sequences related to sums of squares

FORMULA

a(n) = A122510(n,n).

a(n) ~ c / (sqrt(n) * r^n), where r = 0.241970723224463308846762732757915397312... (= radius of convergence A166952) and c = 0.716940866073606328... - Vaclav Kotesovec, Apr 14 2018

MATHEMATICA

Table[SeriesCoefficient[EllipticTheta[3, 0, x]^n/(1 - x), {x, 0, n}], {n, 0, 26}]

Table[SeriesCoefficient[1/(1 - x) Sum[x^k^2, {k, -n, n}]^n, {x, 0, n}], {n, 0, 26}]

CROSSREFS

Main diagonal of A122510.

Cf. A000122, A001650, A046895, A057655, A066535, A117609, A302861, A066536, A166952.

Sequence in context: A147242 A148924 A113994 * A217639 A328080 A148925

Adjacent sequences: A302857 A302858 A302859 * A302861 A302862 A302863

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Apr 14 2018

STATUS

approved