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A302861 a(n) = [x^(n^2)] theta_3(x)^n/(1 - x), where theta_3() is the Jacobi theta function. 4
1, 3, 13, 123, 1281, 16875, 252673, 4031123, 70554353, 1318315075, 26107328109, 549772933959, 12147113355505, 280978137279483, 6780378828922333, 169829490474843659, 4409771551548703649, 118361723203178140163, 3277041835527134201777, 93455465161026267454527 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

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

LINKS

Table of n, a(n) for n=0..19.

Eric Weisstein's World of Mathematics, Jacobi Theta Functions

Index entries for sequences related to sums of squares

FORMULA

a(n) = A122510(n,n^2).

MATHEMATICA

Table[SeriesCoefficient[EllipticTheta[3, 0, x]^n/(1 - x), {x, 0, n^2}], {n, 0, 19}]

Table[SeriesCoefficient[1/(1 - x) Sum[x^k^2, {k, -n, n}]^n, {x, 0, n^2}], {n, 0, 19}]

CROSSREFS

Main diagonal of A302997.

Cf. A000122, A000328, A000605, A055410, A055411, A055412, A055413, A055414, A055415, A055416, A122510, A232173, A302860.

Sequence in context: A121921 A191955 A241458 * A182864 A208590 A228648

Adjacent sequences: A302858 A302859 A302860 * A302862 A302863 A302864

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Apr 14 2018

STATUS

approved

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Last modified December 5 21:40 EST 2022. Contains 358594 sequences. (Running on oeis4.)