A001336 Number of n-step self-avoiding walks on f.c.c. lattice. (Formerly M4867 N2082)

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

Offset

0,2

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.

Sequence in context: A165150 A002921 A199941 * A118475 A190873 A097826

Adjacent sequences: A001333 A001334 A001335 * A001337 A001338 A001339

Keyword

nonn,walk,nice

Author

N. J. A. Sloane

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

Status

approved