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Number of n-step polygons on f.c.c. lattice.
(Formerly M5293 N2302)
7

%I M5293 N2302 #34 Jan 15 2019 02:47:45

%S 0,0,48,264,1680,11640,86352,673104,5424768,44828400,377810928,

%T 3235366752,28074857616,246353214240,2182457514960,19495053028800,

%U 175405981214592

%N Number of n-step polygons on f.c.c. lattice.

%C Number of n-step closed self-avoiding walks starting at the origin. - _Bert Dobbelaere_, Jan 14 2019

%D B. D. Hughes, Random Walks and Random Environments, Oxford 1995, vol. 1, p. 460.

%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H 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 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 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 <a href="/index/Fa#fcc">Index entries for sequences related to f.c.c. lattice</a>

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

%Y Equals 2n*A005398(n).

%Y Cf. A001336.

%K nonn,nice,walk,more

%O 1,3

%A _N. J. A. Sloane_

%E a(15)-a(17) from _Bert Dobbelaere_, Jan 14 2019