%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