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A302860
a(n) = [x^n] theta_3(x)^n/(1 - x), where theta_3() is the Jacobi theta function.
6
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
OFFSET
0,2
COMMENTS
a(n) = number of integer lattice points inside the n-dimensional hypersphere of radius sqrt(n).
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
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Apr 14 2018
STATUS
approved