OFFSET
0,2
COMMENTS
Equivalently, number of points in a hexagonal lattice covered by a circular disk of diameter n if the center of the circle is chosen at the middle between two lattice points. - Hugo Pfoertner, Jan 07 2007
Same as above but "number of disks (r = 1)" instead of "number of points". a(2^n - 1) = A239073(n), n >= 1. See illustration in links. - Kival Ngaokrajang, Apr 06 2014
LINKS
H. v. Eitzen, Table of n, a(n) for n = 0..1000
Kival Ngaokrajang, Illustration of initial terms
FORMULA
a(n)/(n/2)^2 -> Pi*2/sqrt(3).
MATHEMATICA
a[n_] := Sum[dj = Sqrt[Abs[4*n^2 + 6*i - 3*i^2 - 3]]/4; j1 = (1 - 2*i)/4 - dj // Floor; j2 = (1 - 2*i)/4 + dj // Ceiling; Sum[ Boole[i^2 - i - j/2 + i*j + j^2 + 1/4 <= n^2/4], {j, j1, j2}], {i, -n - 1, n + 3}]; Table[a[n], {n, 0, 50}] (* Jean-François Alcover, Jun 06 2013 *)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Klaus Strassburger (strass(AT)ddfi.uni-duesseldorf.de), Jan 10 2000
EXTENSIONS
Edited by N. J. A. Sloane, Jul 03 2008 at the suggestion of R. J. Mathar
STATUS
approved