%I A105062
%S A105062 1,1,2,1,2,2,3,1,2,2,3,2,3,3,4,1,2,2,3,2,3,3,4,2,3,3,4,3,4,4,5,1,2,2,3,
%T A105062 2,3,3,4,2,3,3,4,3,4,4,5,2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,1,2,2,3,2,3,3,
%U A105062 4,2,3,3,4,3,4,4,5,2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,2,3,3,4,3,4,4,5,3,4
%N A105062 Triangle read by rows, based on the morphism f: 1->2, 2->3, 3->4, 4->
               5, 5->6, 6->{6,6,10,7}, 7->8, 8->9, 9->10, 10->11, 11->12, 12->{12,
               12,5,1}. First row is 1. If current row is a,b,c,..., then the next 
               row is a,b,c,...,f(a),f(b),f(c),...
%C A105062 11's and 12's do not show up until the 8th iteration, below that it resembles 
               the lower bi-Kenyons
%C A105062 Level 6 bi-Kenyon substitution sequence.
%H A105062 Richard Kenyon, <a href="http://arXiv.org/abs/math.MG/9505210">The Construction 
               of Self-Similar Tilings</a>
%t A105062 s[n_] := n /. {1 -> 2, 2 -> 3, 3 -> 4, 4 -> 5, 5 -> 6, 6 -> {6, 6, 10, 
               7}, 7 -> 8, 8 -> 9, 9 -> 10, 10 -> 11, 11 -> 12, 12 -> {12, 12, 5, 
               1}}; t[a_] := Join[a, Flatten[s /@ a]]; Flatten[ NestList[t, {1}, 
               6]]
%Y A105062 Cf. A000120, A073058.
%Y A105062 Sequence in context: A105061 A105164 A000120 this_sequence A106487 A105102 
               A105105
%Y A105062 Adjacent sequences: A105059 A105060 A105061 this_sequence A105063 A105064 
               A105065
%K A105062 nonn,tabf
%O A105062 0,3
%A A105062 Roger Bagula (rlbagulatftn(AT)yahoo.com), Apr 05 2005