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

Author

Hugo Pfoertner, Jan 07 2007, Feb 11 2007

Keywords

• nonn

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.

Extensions

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