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Number of n-step tri-directional self-avoiding walks on the hexagonal lattice, after first step.
0

%I #24 Nov 20 2016 19:58:48

%S 3,7,17,41,95,223,523,1201,2781,6445,14731,33859,77899,177523,406115,

%T 929825,2114387,4821367,11001423,24974353,56813401,129315249,

%U 293157759,665688917,1512325105,3424615395

%N Number of n-step tri-directional self-avoiding walks on the hexagonal lattice, after first step.

%C Among the 6 possible directions only 3 are allowed, separated by 120 degrees.

%C We take a first step then count all the n-step walks.

%C This sequence generates a surprising number of primes:

%C * 3: 3

%C * 7: 7

%C * 17: 17

%C * 41: 41

%C 95: 5 19

%C * 223: 223

%C * 523: 523

%C * 1201: 1201

%C 2781: 3 3 3 103

%C 6445: 5 1289

%C * 14731: 14731

%C 33859: 7 7 691

%C * 77899: 77899

%C 177523: 113 1571

%C 406115: 5 81223

%C 929825: 5 5 13 2861

%C 2114387: 11 167 1151

%C 4821367: 1229 3923

%C 11001423: 3 3667141

%C * 24974353: 24974353

%C 56813401: 19 59 59 859

%C 129315249: 3 3 7 101 20323

%C 293157759: 3 97719253

%C 665688917: 59 11282863

%C 1512325105: 5 523 578327

%C 3424615395: 3 5 12497 18269

%F a(n) = A272265(n)/3.

%Y Cf. A272265.

%K nonn,walk

%O 1,1

%A _Francois Alcover_, May 05 2016