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

0,2

Links

Table of n, a(n) for n=0..39.

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

Cf. A001411, A077482, A173380, A334877, A336662.

Sequence in context: A309181 A140466 A343421 * A368614 A330992 A246067

Adjacent sequences: A337350 A337351 A337352 * A337354 A337355 A337356

Keyword

nonn,walk

Author

Scott R. Shannon, Aug 24 2020

Status

approved