A057961 Number of points in square lattice covered by a disc centered at (0,0) as its radius increases.

1, 5, 9, 13, 21, 25, 29, 37, 45, 49, 57, 61, 69, 81, 89, 97, 101, 109, 113, 121, 129, 137, 145, 149, 161, 169, 177, 185, 193, 197, 213, 221, 225, 233, 241, 249, 253, 261, 277, 285, 293, 301, 305, 317, 325, 333, 341, 349, 357, 365, 373, 377, 385, 401, 405, 421

Offset: 1

Author

Ken Takusagawa, Oct 15 2000

Keywords

• easy
• nonn

Comments

Useful for rasterizing circles.

Conjecture: the number of lattice points in a quadrant of the disk is equal to A000592(n-1). - L. Edson Jeffery, Feb 10 2014

Examples

			a(2)=5 because (0,0); (0,1); (0,-1); (1,0); (-1,0) are covered by any disc of radius between 1 and sqrt(2).
		

References

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

Links

• T. D. Noe, Table of n, a(n) for n=1..1000
• L. Edson Jeffery, Illustration of first few terms.

Crossrefs

Cf. A004018, A004020, A005883, A057962. Distinct terms of A057655.

Cf. A000404, A001481, A232499.

Programs

Mathematica

max = 100; A001481 = Select[Range[0, 4*max], SquaresR[2, #] != 0 &]; Table[SquaresR[2, A001481[[n]]], {n, 1, max}] // Accumulate (* Jean-François Alcover, Oct 04 2013 *)