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A001337 Number of n-step polygons on f.c.c. lattice.
(Formerly M5293 N2302)
7
0, 0, 48, 264, 1680, 11640, 86352, 673104, 5424768, 44828400, 377810928, 3235366752, 28074857616, 246353214240, 2182457514960, 19495053028800, 175405981214592 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
COMMENTS
Number of n-step closed self-avoiding walks starting at the origin. - Bert Dobbelaere, Jan 14 2019
REFERENCES
B. D. Hughes, Random Walks and Random Environments, Oxford 1995, vol. 1, p. 460.
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
M. E. Fisher and M. F. Sykes, Excluded-volume problem and the Ising model of ferromagnetism, Phys. Rev. 114 (1959), 45-58.
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.
CROSSREFS
Equals 12*A003287(n-1), n > 1.
Equals 2n*A005398(n).
Cf. A001336.
Sequence in context: A275406 A205469 A115056 * A259993 A205747 A173121
KEYWORD
nonn,nice,walk,more
AUTHOR
EXTENSIONS
a(15)-a(17) from Bert Dobbelaere, Jan 14 2019
STATUS
approved

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Last modified May 30 16:00 EDT 2024. Contains 372968 sequences. (Running on oeis4.)