This site is supported by donations to The OEIS Foundation.



(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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, 197517813636, 767766750564, 2992650987408, 11694675166500, 45807740881032 (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.


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).


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


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

Cf. A001334.

Sequence in context: A230355 A063975 A227895 * A206026 A145899 A172011

Adjacent sequences:  A001332 A001333 A001334 * A001336 A001337 A001338




N. J. A. Sloane


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

a(26) from Bert Dobbelaere, Jan 15 2019



Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 19 06:34 EST 2019. Contains 329310 sequences. (Running on oeis4.)