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.

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

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 2-dimensional 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: A257335 A152211 A309805 * A368824 A336903 A155171

Adjacent sequences: A125849 A125850 A125851 * A125853 A125854 A125855

Keyword

nonn

Author

Hugo Pfoertner, Jan 07 2007, Feb 11 2007

Extensions

More terms copied from b-file by Hagen von Eitzen, Jun 17 2009

Status

approved