A005398 -id:A005398 - cp's OEIS frontend

A003287 Number of n-step self-avoiding walks on f.c.c. lattice from (0,0,0) to (0,1,1).

1, 4, 22, 140, 970, 7196, 56092, 452064, 3735700, 31484244, 269613896, 2339571468, 20529434520, 181871459580, 1624587752400, 14617165101216

Offset: 1

N. J. A. Sloane

Cf. A001337.

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

D. S. McKenzie, The end-to-end length distribution of self-avoiding walks, J. Phys. A 6 (1973), 338-352.
Index entries for sequences related to f.c.c. lattice

Equals A001337(n+1) / 12 for n > 1.
Equals (n+1) * A005398(n+1) / 6 for n > 1.
Cf. A003288, A005543, A005544, A005545, A005546, A005547, A005548.

A001337 = Cases[Import["https://oeis.org/A001337/b001337.txt", "Table"], {, }][[All, 2]];
a[n_] := If[n == 1, 1, A001337[[n + 1]]/12];
a /@ Range[16] (* Jean-François Alcover, Jan 20 2020 *)

One more term and title improved by Sean A. Irvine, Feb 15 2016

a(15)-a(16) from Bert Dobbelaere, Jan 14 2019

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

Original entry on oeis.org

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

Offset: 1

N. J. A. Sloane

Number of n-step closed self-avoiding walks starting at the origin. - Bert Dobbelaere, Jan 14 2019

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).

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

Equals 12*A003287(n-1), n > 1.
Equals 2n*A005398(n).
Cf. A001336.

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

cp's OEIS Frontend

A003287 Number of n-step self-avoiding walks on f.c.c. lattice from (0,0,0) to (0,1,1).

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