

A125852


Number of points in a hexagonal lattice covered by a circular disk of diameter n if the center of the circle is chosen such that the disk covers the maximum possible number of lattice points.


10



2, 7, 10, 19, 24, 37, 48, 61, 77, 94, 115, 134, 157, 187, 208, 241, 265, 301, 330, 367, 406, 444, 486, 527, 572, 617, 665, 721, 769, 825, 877, 935, 993, 1054, 1117, 1182, 1249, 1316, 1385, 1459, 1531, 1615, 1684, 1765, 1842, 1925, 2011, 2096, 2187, 2276
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OFFSET

1,1


COMMENTS

a(n)>=max(A053416(n),A053479(n),A053417(n)). a(n) is an upper bound for the number of segments of a self avoiding path on the 2dimensional triangular lattice such that the path fits into a circle of diameter n. A122226(n)<=a(n).


LINKS

H. v. Eitzen, Table of n, a(n) for n=1..1000
Index entries for sequences related to A2 = hexagonal = triangular lattice
Hugo Pfoertner, Maximum number of points in the hexagonal lattice covered by circular disks. Illustrations.


CROSSREFS

Cf. A053416, A053479, A053417, A125851, A122226. The corresponding sequences for the square lattice and the honeycomb net are A123690 and A127406, respectively.
Sequence in context: A240469 A257335 A152211 * A155171 A049830 A270879
Adjacent sequences: A125849 A125850 A125851 * A125853 A125854 A125855


KEYWORD

nonn


AUTHOR

Hugo Pfoertner, Jan 07 2007, Feb 11 2007


EXTENSIONS

More terms copied from bfile by Hagen von Eitzen, Jun 17 2009


STATUS

approved



