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%I M4406 N1860 #47 Sep 15 2019 13:48:31
%S 1,7,33,123,257,515,925,1419,2109,3071,4169,5575,7153,9171,11513,
%T 14147,17077,20479,24405,28671,33401,38911,44473,50883,57777,65267,
%U 73525,82519,91965,101943,113081,124487,137065,150555,164517,179579,195269,212095
%N Number of points of norm <= n in cubic lattice.
%D J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 107.
%D H. Gupta, A Table of Values of N_3(t), Proc. National Institute of Sciences of India, 13 (1947), 35-63.
%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H T. D. Noe, <a href="/A000605/b000605.txt">Table of n, a(n) for n=0..500</a>
%H W. Fraser and C. C. Gotlieb, <a href="http://dx.doi.org/10.1090/S0025-5718-1962-0155788-9">A calculation of the number of lattice points in the circle and sphere</a>, Math. Comp., 16 (1962), 282-290.
%H Z. C. Holden, R. M. Richard, J. M. Herbert, <a href="http://dx.doi.org/10.1063/1.4850655">Periodic boundary conditions for QM/MM calculations: Ewald summation for extended Gaussian basis sets</a>, The Journal of Chemical Physics, J. Chem. Phys. 139, 244108 (2013).
%F a(n) = A117609(n^2). - _R. J. Mathar_, Apr 21 2010
%F a(n) = [x^(n^2)] theta_3(x)^3/(1 - x), where theta_3() is the Jacobi theta function. - _Ilya Gutkovskiy_, Apr 14 2018
%t Table[Sum[SquaresR[3, k], {k, 0, n^2}], {n, 0, 37}]
%o (C)
%o int A000605(int i)
%o {
%o const int ring = i*i;
%o int result = 0;
%o for (int a = -i; a <= i; a++)
%o for (int b = -i; b <= i; b++)
%o for (int c = -i; c <= i; c++)
%o if ( ring >= a*a+b*b+c*c ) result++;
%o return result;
%o } /* _Oskar Wieland_, Apr 08 2013 */
%o (PARI)
%o N=66; q='q+O('q^(N^2));
%o t=Vec((eta(q^2)^5/(eta(q)^2*eta(q^4)^2))^3/(1-q)); /* A117609 */
%o vector(sqrtint(#t),n,t[(n-1)^2+1])
%o /* _Joerg Arndt_, Apr 08 2013 */
%Y Column k=3 of A302997.
%Y Cf. A117609 (number of lattice points inside the ball x^2+y^2+z^2 <= n).
%K nonn
%O 0,2
%A _N. J. A. Sloane_
%E More terms from _David W. Wilson_, May 22 2000
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