A302861 a(n) = [x^(n^2)] theta_3(x)^n/(1 - x), where theta_3() is the Jacobi theta function.

1, 3, 13, 123, 1281, 16875, 252673, 4031123, 70554353, 1318315075, 26107328109, 549772933959, 12147113355505, 280978137279483, 6780378828922333, 169829490474843659, 4409771551548703649, 118361723203178140163, 3277041835527134201777, 93455465161026267454527

Offset: 0

Author

Ilya Gutkovskiy, Apr 14 2018

Keywords

• nonn

Comments

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

Links

• Eric Weisstein's World of Mathematics, Jacobi Theta Functions
• Index entries for sequences related to sums of squares

Crossrefs

Main diagonal of A302997.

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

Programs

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}]

Formula

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