A060379 Number of self-avoiding polygons on the 2-dimensional square lattice with perimeter 2n with at most 4 horizontal edges in each vertical cross-section.

1, 2, 7, 28, 124, 588, 2938, 15266, 81770, 448698, 2510813, 14277838, 82286365, 479610362, 2822332127, 16745262798

Offset

2,2

Links

Table of n, a(n) for n=2..17.

Doron Zeilberger, The Umbral Transfer-Matrix Method. IV. Counting Self-AvoidingPolygons and walks; Local copy [Pdf file only, no active links]

Formula

See Appendix 2 of the reference (a 7-page system of linear functional equations for 5 unknown generating functions, one of which is the desired generating function).

Example

a(3) = 2 because there are 2 self-avoiding polygons of perimeter 2*3 with at most 4 horizontal edges per vertical cross-section.

Crossrefs

Cf. A005435, A002931.

Sequence in context: A215973 A143927 A253787 * A002931 A088702 A112565

Adjacent sequences: A060376 A060377 A060378 * A060380 A060381 A060382

Keyword

hard,more,nonn

Author

Doron Zeilberger, Apr 03 2001

Status

approved