All Self-Avoiding Paths Through a 2-D Grid

There are 2 self-avoiding (non-self-intersecting) paths through a 1 x 1 grid:
2 paths, 1 x 1 grid

12 paths through a 2 x 2 grid:
12 paths, 2 x 2 grid

184 paths through a 3 x 3 grid:
184 paths, 3 x 3 grid

While we're on the subject, there seem to be 18 self-avoiding paths through a 1 x 1 x 1 lattice:
18 paths, 1 x 1 x 1 lattice

156 paths through a 2 x 1 x 1 lattice:
156 paths, 2 x 1 x 1 lattice

Copyright © 1998-2002 by Robert M. Dickau, I guess.

See also "Self-avoiding Walks of a Rook on a Chessboard", by Steven Finch.

[ home ] || [ mail rmd ] || [ 980319 ]

http://www.prairienet.org/~pops/allpaths.html