A337353 Number of n-step self-avoiding walks on a square lattice where no step can be in the same direction as the previous step.
1, 4, 8, 16, 24, 40, 64, 104, 168, 272, 440, 712, 1128, 1808, 2896, 4640, 7368, 11744, 18752, 29920, 47376, 75304, 119824, 190632, 301488, 478160, 759056, 1204848, 1903576, 3014272, 4776504, 7568688, 11947976, 18895760, 29901592, 47317080, 74643504, 117930520, 186413728, 294666160
Offset: 0
Examples
a(5) = 40. The five possible 5-step walks in the first quadrant are: . +--+ +--+ +--+ +--+ | | | | +--+ +--+ +--+ +--+ +--+ | | | | | | x--+ x--+ x--+ x--+ x--+ +--+ . Each of these can be taken in eight ways on the square lattice, giving 40 in total.
Links
- A. J. Guttmann and A. R. Conway, Self-Avoiding Walks and Polygons, Annals of Combinatorics 5 (2001) 319-345.
Formula
a(n) = 4*A336662(n).
Comments