

A053416


Circle numbers (version 4): a(n)= number of points (i+j/2,j*sqrt(3)/2), i,j integers (triangular grid) contained in a circle of diameter n, centered at (0,0).


14



1, 1, 7, 7, 19, 19, 37, 43, 61, 73, 91, 109, 127, 151, 187, 199, 241, 253, 301, 313, 367, 397, 439, 475, 517, 571, 613, 661, 721, 757, 823, 859, 931, 979, 1045, 1111, 1165, 1237, 1303, 1381, 1459, 1519, 1615, 1663, 1765, 1813, 1921, 1993, 2083, 2173, 2263
(list;
graph;
refs;
listen;
history;
text;
internal format)



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
Index entries for sequences related to A2 = hexagonal = triangular lattice


FORMULA

a(n)/(n/2)^2>Pi*2/sqrt(3)


MATHEMATICA

a[n_] := (m = Ceiling[n/2] + 3; Sum[Boole[ 4*(i^2 + i*j + j^2) <= n^2], {i, m, m}, {j, m, m}] ); Table[a[n], {n, 0, 50}] (* JeanFrançois Alcover, Jun 06 2013 *)


CROSSREFS

Cf. A003215, A125849, A125850, A125851, A125852.
Cf. A053411, A053414, A053415, A053417.
Sequence in context: A070919 A070847 A195863 * A213031 A299453 A300091
Adjacent sequences: A053413 A053414 A053415 * A053417 A053418 A053419


KEYWORD

easy,nonn


AUTHOR

Klaus Strassburger (strass(AT)ddfi.uniduesseldorf.de), Jan 10 2000


EXTENSIONS

Edited by N. J. A. Sloane, Jul 03 2008 at the suggestion of R. J. Mathar


STATUS

approved



