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A001334 Number of n-step self-avoiding walks on hexagonal [ =triangular ] lattice.
(Formerly M4197 N1751)
5
1, 6, 30, 138, 618, 2730, 11946, 51882, 224130, 964134, 4133166, 17668938, 75355206, 320734686, 1362791250, 5781765582, 24497330322, 103673967882, 438296739594, 1851231376374, 7812439620678, 32944292555934, 138825972053046 (list; graph; refs; listen; history; internal format)
OFFSET

0,2

COMMENTS

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

REFERENCES

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, Asymptotic analysis of power-series expansions, pp. 1-234 of C. Domb and J. L. Lebowitz, editors, Phase Transitions and Critical Phenomena. Vol. 13, Academic Press, NY, 1989.

A. J. Guttmann and J. Wang, The extension of self-avoiding random walk series in two dimensions, J. Phys. A 24 (1991), 3107-3109.

B. D. Hughes, Random Walks and Random Environments, Oxford 1995, vol. 1, p. 459.

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.

D. C. Rapaport, J. Phys. A 18 (1985), L201.

S. Redner, Distribution functions in the interior of polymer chains, J. Phys. A 13 (1980), 3525-3541.

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, Some counting theorems in the theory of the Ising problem and the excluded volume problem, J. Math. Phys., 2 (1961), 52-62.

LINKS

I. Jensen, Table of n, a(n) for n = 0..40 [from the Jensen link below]

I. Jensen, Series Expansions for Self-Avoiding Walks

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

CROSSREFS

Cf. A036418, A192208.

Sequence in context: A034545 A002920 A192208 * A125316 A092439 A082149

Adjacent sequences:  A001331 A001332 A001333 * A001335 A001336 A001337

KEYWORD

nonn,walk,nice

AUTHOR

N. J. A. Sloane (njas(AT)research.att.com).

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Last modified February 14 09:54 EST 2012. Contains 205614 sequences.