%I A105056
%S A105056 1,1,2,1,2,2,3,1,2,2,3,2,3,3,4,1,2,2,3,2,3,3,4,2,3,3,4,3,4,4,4,4,7,5,1,
%T A105056 2,2,3,2,3,3,4,2,3,3,4,3,4,4,4,4,7,5,2,3,3,4,3,4,4,4,4,7,5,3,4,4,4,4,7,
%U A105056 5,4,4,4,7,5,4,4,7,5,4,4,7,5,4,4,7,5,8,6,1,2,2,3,2,3,3,4,2,3,3,4,3,4,4
%N A105056 Triangle read by rows, based on the morphism f: 1->2, 2->3, 3->4, 4->
               {4,4,7,5}, 5->6, 6->7, 7->8, 8->{8,8,3,1}. 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 A105056 This sequence is the next level of substitution suggested in section 
               6 of the Kenyon paper. A tile exists at this level as well.
%H A105056 Richard Kenyon, <a href="http://arXiv.org/abs/math.MG/9505210">The Construction 
               of Self-Similar Tilings</a>
%t A105056 s[n_] := n /. {1 -> 2, 2 -> 3, 3 -> 4, 4 -> {4, 4, 7, 5}, 5 -> 6, 6 -> 
               7, 7 -> 8, 8 -> {8, 8, 3, 1}}; t[a_] := Join[a, Flatten[s /@ a]]; 
               Flatten[ NestList[t, {1}, 6]]
%Y A105056 Cf. A000120, A073058.
%Y A105056 Sequence in context: A105111 A105112 A105113 this_sequence A105061 A105164 
               A000120
%Y A105056 Adjacent sequences: A105053 A105054 A105055 this_sequence A105057 A105058 
               A105059
%K A105056 nonn,tabf
%O A105056 0,3
%A A105056 Roger Bagula (rlbagulatftn(AT)yahoo.com), Apr 04 2005