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A001335 Number of n-step polygons on hexagonal lattice.
(Formerly M4828 N2065)
10

%I M4828 N2065 #46 May 16 2020 03:51:49

%S 1,0,0,12,24,60,180,588,1968,6840,24240,87252,318360,1173744,4366740,

%T 16370700,61780320,234505140,894692736,3429028116,13195862760,

%U 50968206912,197517813636,767766750564,2992650987408,11694675166500,45807740881032

%N Number of n-step polygons on hexagonal lattice.

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

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

%D A. J. Guttmann, personal communication.

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

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

%H M. E. Fisher and M. F. Sykes, <a href="http://dx.doi.org/10.1103/PhysRev.114.45">Excluded-volume problem and the Ising model of ferromagnetism</a>, Phys. Rev. 114 (1959), 45-58.

%H A. J. Guttmann, <a href="https://doi.org/10.1088/0305-4470/17/2/030">On Two-Dimensional Self-Avoiding Random Walks</a>, J. Phys. A 17 (1984), 455-468.

%H B. D. Hughes, Random Walks and Random Environments, vol. 1, Oxford 1995, <a href="/A001334/a001334.pdf">Tables and references for self-avoiding walks counts</a> [Annotated scanned copy of several pages of a preprint or a draft of chapter 7 "The self-avoiding walk"]

%H J. L. Martin, M. F. Sykes and F. T. Hioe, <a href="http://dx.doi.org/10.1063/1.1841242">Probability of initial ring closure for self-avoiding walks on the face-centered cubic and triangular lattices</a>, J. Chem. Phys., 46 (1967), 3478-3481.

%H G. Nebe and N. J. A. Sloane, <a href="http://www.math.rwth-aachen.de/~Gabriele.Nebe/LATTICES/A2.html">Home page for hexagonal (or triangular) lattice A2</a>

%H M. F. Sykes et al., <a href="https://doi.org/10.1088/0305-4470/5/5/007">The number of self-avoiding walks on a lattice</a>, J. Phys. A 5 (1972), 661-666.

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

%Y Cf. A001334.

%K nonn,nice,walk,more

%O 0,4

%A _N. J. A. Sloane_

%E a(22)-a(25) computed from A003289 by _Bert Dobbelaere_, Jan 04 2019

%E a(26) from _Bert Dobbelaere_, Jan 15 2019

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Last modified March 28 15:38 EDT 2024. Contains 371254 sequences. (Running on oeis4.)