A055406 Number of points in N^7 of norm <= n.

1, 8, 106, 702, 3390, 11496, 33792, 83877, 191433, 394251, 766518, 1397065, 2446316, 4076126, 6601783, 10324698, 15776495, 23436651, 34198045, 48828417, 68680634, 94868383, 129404333, 173984393, 231540046, 304058667, 395837165

Offset: 0

Author

David W. Wilson

Keywords

• nonn

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..500

Crossrefs

Column k=7 of A302998.

Programs

Mathematica

a[n_]:=SeriesCoefficient[(1 + EllipticTheta[3, 0, x])^7/(128 (1 - x)), {x, 0, n^2}]; Array[a,27,0] (* Stefano Spezia, Mar 31 2025 *)

Formula

a(n) = [x^(n^2)] (1 + theta_3(x))^7/(128*(1 - x)), where theta_3() is the Jacobi theta function. - Ilya Gutkovskiy, Apr 15 2018