A088702 Number of polygons with polygonal holes on the square lattice enumerated by half-perimeter.

0, 1, 2, 7, 28, 124, 588, 2939, 15292, 82168, 453376, 2558074, 14712038, 86029132, 510455002, 3068304865, 18658787150, 114663168405, 711391109162, 4452321247688, 28090360338572, 178550339417087, 1142799275636690

Offset

1,3

Comments

The polygons and the hole are self-avoiding and mutually-avoiding, i.e., no degree four vertices are allowed. Translations are allowed, rotations and reflections are not allowed. The contribution of the holes to the perimeter is counted. The number of the holes is not limited, possibly no holes.

Links

I. Jensen, Table of n, a(n) for n = 1..43 (from link below)

Anthony J. Guttmann, Iwan Jensen, Ling Heng Wong and Ian G. Enting, Punctured polygons and polyominoes on the square lattice, J. Phys. A, Vol. 33 (2000) 1735-1764.

Iwan Jensen, List of terms

Iwan Jensen, Series expansions for self-avoiding polygons

Crossrefs

Cf. A002931 (self-avoiding polygons), A056634 (self-avoiding polygons with exactly one hole), A056638 (self-avoiding polygons with exactly two holes), A056639 (self-avoiding polygons with exactly three holes), A391197 (any holes allowed).

Sequence in context: A253787 A060379 A002931 * A391197 A112565 A227845

Adjacent sequences: A088699 A088700 A088701 * A088703 A088704 A088705

Keyword

nonn

Author

Markus Voege (markus.voege(AT)inria.fr), Nov 23 2003

Status

approved