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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.

%I A337353 #11 Sep 06 2020 11:05:44
%S A337353 1,4,8,16,24,40,64,104,168,272,440,712,1128,1808,2896,4640,7368,11744,
%T A337353 18752,29920,47376,75304,119824,190632,301488,478160,759056,1204848,
%U A337353 1903576,3014272,4776504,7568688,11947976,18895760,29901592,47317080,74643504,117930520,186413728,294666160
%N 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.
%H A337353 A. J. Guttmann and A. R. Conway, <a href="http://dx.doi.org/10.1007/PL00013842">Self-Avoiding Walks and Polygons</a>, Annals of Combinatorics 5 (2001) 319-345.
%F A337353 a(n) = 4*A336662(n).
%e A337353 a(5) = 40. The five possible 5-step walks in the first quadrant are:
%e A337353 .
%e A337353 +--+   +--+         +--+        +--+
%e A337353 |         |            |        |
%e A337353 +--+      +--+      +--+     +--+       +--+
%e A337353    |         |      |        |          |  |
%e A337353 x--+      x--+   x--+     x--+       x--+  +--+
%e A337353 .
%e A337353 Each of these can be taken in eight ways on the square lattice, giving 40 in total.
%Y A337353 Cf. A001411, A077482, A173380, A334877, A336662.
%K A337353 nonn,walk
%O A337353 0,2
%A A337353 _Scott R. Shannon_, Aug 24 2020