A003287 Number of n-step self-avoiding walks on f.c.c. lattice from (0,0,0) to (0,1,1). (Formerly M3588)

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

Offset

1,2

Comments

Cf. A001337.

References

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

Links

Table of n, a(n) for n=1..16.

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

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 *)

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.

Sequence in context: A002293 A181784 A369126 * A077056 A227404 A366677

Adjacent sequences: A003284 A003285 A003286 * A003288 A003289 A003290

Keyword

nonn,walk,more

Author

N. J. A. Sloane

Extensions

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

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

Status

approved