

A001335


Number of nstep polygons on hexagonal lattice.
(Formerly M4828 N2065)


10



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
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OFFSET

1,3


COMMENTS

The hexagonal lattice is the familiar 2dimensional 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=1..26.
M. E. Fisher and M. F. Sykes, Excludedvolume problem and the Ising model of ferromagnetism, Phys. Rev. 114 (1959), 4558.
A. J. Guttmann, On TwoDimensional SelfAvoiding Random Walks, J. Phys. A 17 (1984), 455468.
B. D. Hughes, Random Walks and Random Environments, vol. 1, Oxford 1995, Tables and references for selfavoiding walks counts [Annotated scanned copy of several pages of a preprint or a draft of chapter 7 "The selfavoiding walk"]
J. L. Martin, M. F. Sykes and F. T. Hioe, Probability of initial ring closure for selfavoiding walks on the facecentered cubic and triangular lattices, J. Chem. Phys., 46 (1967), 34783481.
G. Nebe and N. J. A. Sloane, Home page for hexagonal (or triangular) lattice A2
M. F. Sykes et al., The number of selfavoiding walks on a lattice, J. Phys. A 5 (1972), 661666.


CROSSREFS

Equals 6*A003289(n1), n > 2.
Cf. A001334.
Sequence in context: A230355 A063975 A227895 * A206026 A145899 A172011
Adjacent sequences: A001332 A001333 A001334 * A001336 A001337 A001338


KEYWORD

nonn,nice,walk,more,changed


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



