A093836 - OEIS

%I #16 May 29 2015 11:53:22

%S 5,13,29,49,81,113,149,197,253,317,377,49,529,613,709,797,53,1009,

%T 1129,1257,1373,1517,1653,1793,1961,2121,763,2453,2629,2821,3001,3209,

%U 3409,3625,3853,1351,4293,4513,4777,201,5261,5525,5789,6077,6361,6625

%N Numerator of A000328(n)/n^2, where A000328(n) is the number of lattice points (x,y) with x^2 + y^2 <= n^2.

%C First differs from A000328 at n=12: A000328(12) = 441, a(12) = 49.

%H Robert Israel, <a href="/A093836/b093836.txt">Table of n, a(n) for n = 1..10000</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/GausssCircleProblem.html">Gauss's Circle Problem</a>

%p N:= 100: # to get a(1) to a(N)

%p B:= Array(1..N);

%p for i from 0 to N do

%p   for j from i while i^2 + j^2 <= N^2 do

%p      v:= ceil(sqrt(i^2+j^2));

%p      if [i,j] = [0,0] then m:= 1; v:= 1

%p      elif i=0 or i=j then m:= 4

%p      else m:= 8

%p      fi;

%p      B[v]:= B[v]+m;

%p   od

%p od:

%p A000328:= ListTools:-PartialSums(convert(B,list)):

%p seq(numer(A000328[n]/n^2),n=1..N); # _Robert Israel_, May 28 2015

%Y Cf. A093837 (denominators), A000328, A093832.

%K nonn,frac

%O 1,1

%A _Eric W. Weisstein_, Apr 17 2004

%E Definition edited by _Robert Israel_, May 28 2015