cp's OEIS Frontend

A272480 Number of n-step tri-directional self-avoiding walks on the hexagonal lattice, after first step.

%I A272480 #24 Nov 20 2016 19:58:48
%S A272480 3,7,17,41,95,223,523,1201,2781,6445,14731,33859,77899,177523,406115,
%T A272480 929825,2114387,4821367,11001423,24974353,56813401,129315249,
%U A272480 293157759,665688917,1512325105,3424615395
%N A272480 Number of n-step tri-directional self-avoiding walks on the hexagonal lattice, after first step.
%C A272480 Among the 6 possible directions only 3 are allowed, separated by 120 degrees.
%C A272480 We take a first step then count all the n-step walks.
%C A272480 This sequence generates a surprising number of primes:
%C A272480 *   3: 3
%C A272480 *   7: 7
%C A272480 *   17: 17
%C A272480 *   41: 41
%C A272480     95: 5 19
%C A272480 *   223: 223
%C A272480 *   523: 523
%C A272480 *   1201: 1201
%C A272480     2781: 3 3 3 103
%C A272480     6445: 5 1289
%C A272480 *   14731: 14731
%C A272480     33859: 7 7 691
%C A272480 *   77899: 77899
%C A272480     177523: 113 1571
%C A272480     406115: 5 81223
%C A272480     929825: 5 5 13 2861
%C A272480     2114387: 11 167 1151
%C A272480     4821367: 1229 3923
%C A272480     11001423: 3 3667141
%C A272480 *   24974353: 24974353
%C A272480     56813401: 19 59 59 859
%C A272480     129315249: 3 3 7 101 20323
%C A272480     293157759: 3 97719253
%C A272480     665688917: 59 11282863
%C A272480     1512325105: 5 523 578327
%C A272480     3424615395: 3 5 12497 18269
%F A272480 a(n) = A272265(n)/3.
%Y A272480 Cf. A272265.
%K A272480 nonn,walk
%O A272480 1,1
%A A272480 _Francois Alcover_, May 05 2016