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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.
9
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
0,2
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).
EXAMPLE
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.
CROSSREFS
KEYWORD
nonn,walk
AUTHOR
Scott R. Shannon, Aug 24 2020
STATUS
approved