login
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),...
0

%I #13 Feb 24 2023 15:44:20

%S 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 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 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 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 Six-symbol substitution of the bi-Kenyon type.

%H Richard Kenyon, <a href="http://arXiv.org/abs/math.MG/9505210">The Construction of Self-Similar Tilings</a>

%e Triangle begins:

%e 1,

%e 1, 2,

%e 1, 2, 2, 3,

%e 1, 2, 2, 3, 2, 3, 3, 6, 5, 4,

%e 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 ...

%t 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 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 Cf. A103684.

%K nonn,tabf

%O 0,3

%A _Roger L. Bagula_, Apr 07 2005