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
The conjecture is true because a(n) is the cumulative sum of A105352(n), which is the number of distinct squared hypotenuses that are the radius of the disc whose center is (0,0) as it increases, once that a(A047808(n))=A000328(n) for n>=1; see A000161 and A000925. - Flávio V. Fernandes, Jan 09 2026
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
KEYWORD
easy,nonn
AUTHOR
Ken Takusagawa, Oct 15 2000
STATUS
approved