A057962 - OEIS

%I #2 Mar 31 2012 10:24:40

%S 4,12,16,24,32,44,52,60,68,76,80,88,96,112,120,124,140,148,156,164,

%T 172,180,188,192,208,216,232,240,248,256,268,276,284,300,308,316,332,

%U 348,360,368,376,384,392,400,408,424,432,440,448,460,468,484,492,500

%N Number of points (x,y) in square lattice with (x-1/2)^2+(y-1/2)^2 <= n.

%C Always a multiple of 4. Useful for rasterizing circles.

%D J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 106.

%e a(2)=12 because (-1,0); (-1,1); (0,-1); (0,0); (0,1); (0,2); (1,-1); (1,0); (1,1); (1,2); (2,0); (2,1) are covered by any disc of radius between sqrt(2.5) and sqrt(4.5) and centered at (0.5,0.5).

%Y Cf. A057961, A004018, A004020. Partial sums of A005883.

%K easy,nonn

%O 1,1

%A _Ken Takusagawa_, Oct 15 2000