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A105105 Triangle read by rows, based on the morphism f: 1-> 2->3 3->{6,5,4} 4->5 5->6 6->{3,2,1}. 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),...

%I A105105 #13 Feb 24 2023 15:44:20
%S A105105 1,1,2,1,2,2,3,1,2,2,3,2,3,3,6,5,4,1,2,2,3,2,3,3,6,5,4,2,3,3,6,5,4,3,
%T A105105 6,5,4,6,5,4,3,2,1,6,5,1,2,2,3,2,3,3,6,5,4,2,3,3,6,5,4,3,6,5,4,6,5,4,
%U A105105 3,2,1,6,5,2,3,3,6,5,4,3,6,5,4,6,5,4,3,2,1,6,5,3,6,5,4,6,5,4,3,2,1,6,5,6,5
%N A105105 Triangle read by rows, based on the morphism f: 1-> 2->3 3->{6,5,4} 4->5 5->6 6->{3,2,1}. 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 A105105 Six-symbol substitution of the bi-Kenyon type.
%H A105105 Richard Kenyon, <a href="http://arXiv.org/abs/math.MG/9505210">The Construction of Self-Similar Tilings</a>
%e A105105 Triangle begins:
%e A105105 1,
%e A105105 1, 2,
%e A105105 1, 2, 2, 3,
%e A105105 1, 2, 2, 3, 2, 3, 3, 6, 5, 4,
%e A105105 1, 2, 2, 3, 2, 3, 3, 6, 5, 4, 2, 3, 3, 6, 5, 4, 3, 6, 5, 4, 6, 5, 4, 3, 2, 1, 6, 5,
%e A105105 ...
%t A105105 s[n_] := n /. {1 -> 2, 2 -> 3, 3 -> {6, 5, 4}, 4 -> 5, 5 -> 6, 6 -> {3, 2, 1}}; t[a_] := Join[a, Flatten[s /@ a]]; Flatten[ NestList[t, {1}, 5]]
%t A105105 NestList[ Flatten[ Join[ #, # /. {1 -> {2}, 2 ->{3}, 3 ->{6,5,4}, 4 ->{5}, 5-> {6}, 6-> {3,2,1}} ]] &, {1}, 5] // Flatten (* _Robert G. Wilson v_, Jun 05 2014 *)
%Y A105105 Cf. A103684.
%K A105105 nonn,tabf
%O A105105 0,3
%A A105105 _Roger L. Bagula_, Apr 07 2005