A001336 Number of n-step self-avoiding walks on f.c.c. lattice.

1, 12, 132, 1404, 14700, 152532, 1573716, 16172148, 165697044, 1693773924, 17281929564, 176064704412, 1791455071068, 18208650297396, 184907370618612, 1876240018679868, 19024942249966812, 192794447005403916, 1952681556794601732, 19767824914170222996

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• walk
• nice

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

• Andrey Zabolotskiy, Table of n, a(n) for n = 0..24 (from Schram et al.)
• 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.
• S. McKenzie, Self-avoiding walks on the face-centered cubic lattice, J. Phys. A 12 (1979), L267-L270.
• S. Redner, Distribution functions in the interior of polymer chains, J. Phys. A 13 (1980), 3525-3541, doi:10.1088/0305-4470/13/11/023.
• Raoul D. Schram, Gerard T. Barkema, Rob H. Bisseling and Nathan Clisby, Exact enumeration of self-avoiding walks on BCC and FCC lattices, J. Stat. Mech. (2017) 083208; arXiv:1703.09340 [cond-mat.stat-mech], 2017. See Table II.
• 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.
• Index entries for sequences related to f.c.c. lattice

Crossrefs

Cf. A001411, A001412, A001334, A001666, A001337.

Extensions

a(15) from Bert Dobbelaere, Jan 13 2019

Terms a(16) and beyond from Schram et al. added by Andrey Zabolotskiy, Feb 02 2022