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

Author

N. J. A. Sloane

Keywords

• nonn
• walk
• more

Comments

Cf. A001337.

References

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

Links

• 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

Crossrefs

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.

Programs

Mathematica

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 *)

Extensions

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

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