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A055416 Number of points in Z^10 of norm <= n. 6

%I #15 Sep 15 2019 13:49:13

%S 1,21,4541,198765,3083569,27634481,164379601,759891589,2839094517,

%T 9183188589,26107328109,67602028569,160441685209,357086356401,

%U 746545031221,1487788785845,2829595966381,5188248484757,9170828884817

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

%C 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

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

%H Andrew Howroyd, <a href="/A055416/b055416.txt">Table of n, a(n) for n = 0..500</a>

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

%e To check that a(2) = 4541:

%e norm^2 # total

%e 0 1 1

%e 1 20 21

%e 2 180 201

%e 3 960 1161

%e 4 3380 4541

%Y Column k=10 of A302997.

%K nonn

%O 0,2

%A _David W. Wilson_

%E Edited by _N. J. A. Sloane_, Sep 29 2007

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Last modified April 16 11:35 EDT 2024. Contains 371711 sequences. (Running on oeis4.)