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A001335 Number of n-step polygons on hexagonal lattice.
(Formerly M4828 N2065)
0, 0, 12, 24, 60, 180, 588, 1968, 6840, 24240, 87252, 318360, 1173744, 4366740, 16370700, 61780320, 234505140, 894692736, 3429028116, 13195862760, 50968206912 (list; graph; refs; listen; history; text; internal format)



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


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, personal communication.

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

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.

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).

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


Table of n, a(n) for n=1..21.

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

Unknown author, Tables of self-avoiding walks, [Annotated scanned copy. Unfortunately the author and title of this document have been mislaid]


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

Sequence in context: A230355 A063975 A227895 * A206026 A145899 A172011

Adjacent sequences:  A001332 A001333 A001334 * A001336 A001337 A001338




N. J. A. Sloane



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Last modified October 20 18:08 EDT 2018. Contains 316401 sequences. (Running on oeis4.)