cp's OEIS Frontend

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

%I A001336 M4867 N2082 #46 Jul 25 2023 19:27:01
%S A001336 1,12,132,1404,14700,152532,1573716,16172148,165697044,1693773924,
%T A001336 17281929564,176064704412,1791455071068,18208650297396,
%U A001336 184907370618612,1876240018679868,19024942249966812,192794447005403916,1952681556794601732,19767824914170222996
%N A001336 Number of n-step self-avoiding walks on f.c.c. lattice.
%D A001336 B. D. Hughes, Random Walks and Random Environments, Oxford 1995, vol. 1, p. 460.
%D A001336 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D A001336 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A001336 Andrey Zabolotskiy, <a href="/A001336/b001336.txt">Table of n, a(n) for n = 0..24</a> (from Schram et al.)
%H A001336 M. E. Fisher and M. F. Sykes, <a href="http://dx.doi.org/10.1103/PhysRev.114.45">Excluded-volume problem and the Ising model of ferromagnetism</a>, Phys. Rev. 114 (1959), 45-58.
%H A001336 B. D. Hughes, Random Walks and Random Environments, vol. 1, Oxford 1995, <a href="/A001334/a001334.pdf">Tables and references for self-avoiding walks counts</a> [Annotated scanned copy of several pages of a preprint or a draft of chapter 7 "The self-avoiding walk"]
%H A001336 J. L. Martin, M. F. Sykes and F. T. Hioe, <a href="http://dx.doi.org/10.1063/1.1841242">Probability of initial ring closure for self-avoiding walks on the face-centered cubic and triangular lattices</a>, J. Chem. Phys., 46 (1967), 3478-3481.
%H A001336 S. McKenzie, <a href="https://doi.org/10.1088/0305-4470/12/10/005">Self-avoiding walks on the face-centered cubic lattice</a>, J. Phys. A 12 (1979), L267-L270.
%H A001336 S. Redner, <a href="http://physics.bu.edu/~redner/pubs/pdf/jpa13p3525.pdf">Distribution functions in the interior of polymer chains</a>, J. Phys. A 13 (1980), 3525-3541, doi:10.1088/0305-4470/13/11/023.
%H A001336 Raoul D. Schram, Gerard T. Barkema, Rob H. Bisseling and Nathan Clisby, <a href="https://doi.org/10.1088/1742-5468/aa819f">Exact enumeration of self-avoiding walks on BCC and FCC lattices</a>, J. Stat. Mech. (2017) 083208; arXiv:<a href="https://arxiv.org/abs/1703.09340">1703.09340</a> [cond-mat.stat-mech], 2017. See Table II.
%H A001336 M. F. Sykes, <a href="http://dx.doi.org/10.1063/1.1724212">Some counting theorems in the theory of the Ising problem and the excluded volume problem</a>, J. Math. Phys., 2 (1961), 52-62.
%H A001336 <a href="/index/Fa#fcc">Index entries for sequences related to f.c.c. lattice</a>
%Y A001336 Cf. A001411, A001412, A001334, A001666, A001337.
%K A001336 nonn,walk,nice
%O A001336 0,2
%A A001336 _N. J. A. Sloane_
%E A001336 a(15) from _Bert Dobbelaere_, Jan 13 2019
%E A001336 Terms a(16) and beyond from Schram et al. added by _Andrey Zabolotskiy_, Feb 02 2022