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A057961
Number of points in square lattice covered by a disc centered at (0,0) as its radius increases.
12
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.
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.
Sequence in context: A314790 A314791 A259568 * A314792 A089217 A166049
KEYWORD
easy,nonn
AUTHOR
Ken Takusagawa, Oct 15 2000
STATUS
approved