A036418 Number of self-avoiding polygons with perimeter n on hexagonal [ =triangular ] lattice.

0, 0, 2, 3, 6, 15, 42, 123, 380, 1212, 3966, 13265, 45144, 155955, 545690, 1930635, 6897210, 24852576, 90237582, 329896569, 1213528736, 4489041219, 16690581534, 62346895571, 233893503330, 880918093866, 3329949535934

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• walk

Comments

The hexagonal lattice is the familiar 2-dimensional lattice in which each point has 6 neighbors. This is sometimes called the triangular lattice.

References

• B. D. Hughes, Random Walks and Random Environments, Oxford 1995, vol. 1, p. 459.

Links

• I. Jensen, Table of n, a(n) for n = 1..60
• Iwan Jensen, Self-avoiding walks and polygons on the triangular lattice, arXiv:cond-mat/0409039 [cond-mat.stat-mech], 2004.
• G. Nebe and N. J. A. Sloane, Home page for hexagonal (or triangular) lattice A2
• Index entries for sequences related to A2 = hexagonal = triangular lattice

Crossrefs

Cf. A001334, A284869.