A001337 Number of n-step polygons on f.c.c. lattice. (Formerly M5293 N2302)

0, 0, 48, 264, 1680, 11640, 86352, 673104, 5424768, 44828400, 377810928, 3235366752, 28074857616, 246353214240, 2182457514960, 19495053028800, 175405981214592

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

Table of n, a(n) for n=1..17.

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.

Index entries for sequences related to f.c.c. lattice

Crossrefs

Equals 12*A003287(n-1), n > 1.

Equals 2n*A005398(n).

Cf. A001336.

Sequence in context: A275406 A205469 A115056 * A259993 A205747 A173121

Adjacent sequences: A001334 A001335 A001336 * A001338 A001339 A001340

Keyword

nonn,nice,walk,more

Author

N. J. A. Sloane

Extensions

a(15)-a(17) from Bert Dobbelaere, Jan 14 2019

Status

approved