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

1,2

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

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.

Example

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).

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 *)

Crossrefs

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

Cf. A000404, A001481, A232499.

Sequence in context: A314790 A314791 A259568 * A314792 A089217 A166049

Adjacent sequences: A057958 A057959 A057960 * A057962 A057963 A057964

Keyword

easy,nonn

Author

Ken Takusagawa, Oct 15 2000

Status

approved