OFFSET
0,3
COMMENTS
In other words, number of points in a hexagonal lattice covered by a circle of diameter n if the center of the circle is chosen at a grid point. - Hugo Pfoertner, Jan 07 2007
Same as above but "number of disks (r = 1)" instead of "number of points". 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).
a(n) >= A053458(n). - R. J. Mathar, Nov 22 2022
a(2*n) = A308685(n). - R. J. Mathar, Nov 22 2022
MAPLE
A053416 := proc(d)
local a, j, imin, imax ;
a := 0 ;
for j from -floor(d/sqrt(3)) do
if j^2*3 > d^2 and j> 0 then
break ;
end if;
imin := ceil((-j-sqrt(d^2-3*j^2))/2) ;
imax := floor((-j+sqrt(d^2-3*j^2))/2) ;
a := a+imax-imin+1 ;
end do:
a ;
end proc:
seq(A053416(d), d=0..30) ; # R. J. Mathar, Nov 22 2022
MATHEMATICA
a[n_] := Sum[Boole[4*(i^2 + i*j + j^2) <= n^2], {i, -n, n}, {j, -n, n}];
Table[a[n], {n, 0, 100}] (* Jean-François Alcover, Jun 06 2013, updated Apr 08 2022 to correct a discrepancy wrt b-file noticed by Georg Fischer *)
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