A055416 Number of points in Z^10 of norm <= n.

1, 21, 4541, 198765, 3083569, 27634481, 164379601, 759891589, 2839094517, 9183188589, 26107328109, 67602028569, 160441685209, 357086356401, 746545031221, 1487788785845, 2829595966381, 5188248484757, 9170828884817

Offset: 0

Author

David W. Wilson

Keywords

• nonn

Comments

Here "norm" is being used in the sense of L_2 norm, as opposed to the definition in SPLAG. - N. J. A. Sloane, Sep 29 2007

Examples

			To check that a(2) = 4541:
norm^2 # total
0 1 1
1 20 21
2 180 201
3 960 1161
4 3380 4541
		

References

• J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag.

Links

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

Crossrefs

Column k=10 of A302997.

Formula

a(n) = [x^(n^2)] theta_3(x)^10/(1 - x), where theta_3() is the Jacobi theta function. - Ilya Gutkovskiy, Apr 15 2018

Extensions

Edited by N. J. A. Sloane, Sep 29 2007