Search: id:A000328
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%I A000328 M3829 N1570
%S A000328 1,5,13,29,49,81,113,149,197,253,317,377,441,529,613,709,797,901,1009,
%T A000328 1129,1257,1373,1517,1653,1793,1961,2121,2289,2453,2629,2821,3001,3209,
%U A000328 3409,3625,3853,4053,4293,4513,4777,5025,5261,5525,5789,6077,6361,6625
%N A000328 Number of points of norm <= n^2 in square lattice.
%C A000328 Number of ordered pairs of integers (x,y) with x^2 + y^2 <= n^2.
%C A000328 Or, numerator of N(r)/r^2, where N(r) is the number of lattice points 
               inside a circle of radius r.
%D A000328 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A000328 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A000328 J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", 
               Springer-Verlag, p. 106.
%D A000328 W. Fraser and C. C. Gotlieb, A calculation of the number of lattice points 
               in the circle and sphere, Math. Comp., 16 (1962), 282-290.
%D A000328 H. Gupta, A Table of Values of N_3(t), Proc. National Institute of Sciences 
               of India, 13 (1947), 35-63.
%D A000328 C. D. Olds, A. Lax and G. P. Davidoff, The Geometry of Numbers, Math. 
               Assoc. Amer., 2000, p. 47.
%H A000328 T. D. Noe, <a href="b000328.txt">Table of n, a(n) for n=0..1000</a>
%H A000328 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               GausssCircleProblem.html">Gauss's Circle Problem</a>
%F A000328 a(n) = 1 + 4 * Sum[j=0..oo] [n^2/(4*j+1)] - [n^2/(4*j+3)]. Also a(n) 
               = A057655(n^2). - Max Alekseyev (maxale(AT)gmail.com), Nov 18 2007
%t A000328 Needs["NumberTheory`NumberTheoryFunctions`"]; Table[Sum[SumOfSquaresR[2, 
               k], {k, 0, n^2}], {n, 0, 46}]
%o A000328 (PARI) { a(n) = 1 + 4 * sum(j=0,n^2\4, n^2\(4*j+1) - n^2\(4*j+3) ) } 
               - Max Alekseyev (maxale(AT)gmail.com), Nov 18 2007
%Y A000328 Equals A051132 + A046109. For another version see A057655.
%Y A000328 Cf. A093832, A093837.
%Y A000328 Sequence in context: A130066 A095085 A093836 this_sequence A100438 A129371 
               A130230
%Y A000328 Adjacent sequences: A000325 A000326 A000327 this_sequence A000329 A000330 
               A000331
%K A000328 nonn,easy,nice
%O A000328 0,2
%A A000328 N. J. A. Sloane (njas(AT)research.att.com).
%E A000328 More terms from David W. Wilson (davidwwilson(AT)comcast.net), May 22, 
               2000
%E A000328 Edited by N. J. A. Sloane (njas(AT)research.att.com), Nov 18 2007, at 
               the suggestion of Max Alekseyev.

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