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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

%I #11 Sep 06 2020 11:05:44

%S 1,4,8,16,24,40,64,104,168,272,440,712,1128,1808,2896,4640,7368,11744,

%T 18752,29920,47376,75304,119824,190632,301488,478160,759056,1204848,

%U 1903576,3014272,4776504,7568688,11947976,18895760,29901592,47317080,74643504,117930520,186413728,294666160

%N 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 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 a(n) = 4*A336662(n).

%e a(5) = 40. The five possible 5-step walks in the first quadrant are:

%e .

%e +--+ +--+ +--+ +--+

%e | | | |

%e +--+ +--+ +--+ +--+ +--+

%e | | | | | |

%e x--+ x--+ x--+ x--+ x--+ +--+

%e .

%e Each of these can be taken in eight ways on the square lattice, giving 40 in total.

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

%K nonn,walk

%O 0,2

%A _Scott R. Shannon_, Aug 24 2020