A001335 Number of n-step polygons on hexagonal lattice. (Formerly M4828 N2065)

1, 0, 0, 12, 24, 60, 180, 588, 1968, 6840, 24240, 87252, 318360, 1173744, 4366740, 16370700, 61780320, 234505140, 894692736, 3429028116, 13195862760, 50968206912, 197517813636, 767766750564, 2992650987408, 11694675166500, 45807740881032

Offset

0,4

Comments

A "polygon" is a self-avoiding walk from (0,0) to (0,0).

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

References

A. J. Guttmann, personal communication.

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Table of n, a(n) for n=0..26.

M. E. Fisher and M. F. Sykes, Excluded-volume problem and the Ising model of ferromagnetism, Phys. Rev. 114 (1959), 45-58.

A. J. Guttmann, On Two-Dimensional Self-Avoiding Random Walks, J. Phys. A 17 (1984), 455-468.

B. D. Hughes, Random Walks and Random Environments, vol. 1, Oxford 1995, Tables and references for self-avoiding walks counts [Annotated scanned copy of several pages of a preprint or a draft of chapter 7 "The self-avoiding walk"]

J. L. Martin, M. F. Sykes and F. T. Hioe, Probability of initial ring closure for self-avoiding walks on the face-centered cubic and triangular lattices, J. Chem. Phys., 46 (1967), 3478-3481.

G. Nebe and N. J. A. Sloane, Home page for hexagonal (or triangular) lattice A2

M. F. Sykes et al., The number of self-avoiding walks on a lattice, J. Phys. A 5 (1972), 661-666.

Crossrefs

Equals 6*A003289(n-1), n > 2.

Cf. A001334.

Sequence in context: A330076 A332037 A332039 * A206026 A145899 A172011

Adjacent sequences: A001332 A001333 A001334 * A001336 A001337 A001338

Keyword

nonn,nice,walk,more

Author

N. J. A. Sloane

Extensions

a(22)-a(25) computed from A003289 by Bert Dobbelaere, Jan 04 2019

a(26) from Bert Dobbelaere, Jan 15 2019

Status

approved