

A055416


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


6



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

0,2


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


REFERENCES

J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", SpringerVerlag.


LINKS

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


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


EXAMPLE

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


CROSSREFS

Column k=10 of A302997.
Sequence in context: A250064 A200998 A209473 * A220620 A221120 A203370
Adjacent sequences: A055413 A055414 A055415 * A055417 A055418 A055419


KEYWORD

nonn


AUTHOR

David W. Wilson


EXTENSIONS

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


STATUS

approved



