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A055416 Number of points in Z^10 of norm <= n. 2
1, 21, 4541, 198765, 3083569, 27634481, 164379601, 759891589, 2839094517, 9183188589, 26107328109, 67602028569, 160441685209, 357086356401, 746545031221, 1487788785845, 2829595966381, 5188248484757, 9170828884817 (list; graph; refs; listen; history; text; internal format)
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", Springer-Verlag.

LINKS

Table of n, a(n) for n=0..18.

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

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

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Last modified February 16 03:26 EST 2019. Contains 320140 sequences. (Running on oeis4.)