A001337 Number of n-step polygons on f.c.c. lattice.

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

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• nice
• walk
• more

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

Crossrefs

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

Equals 2n*A005398(n).

Cf. A001336.

Extensions

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