|
%I #6 Mar 12 2014 16:36:46
%S 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,
%T 3,2,3,3,4,2,3,3,4,3,4,4,5,2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,1,2,2,3,2,
%U 3,3,4,2,3,3,4,3,4,4,5,2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,2,3,3,4,3,4,4,5,3,4
%N 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 11's and 12's do not show up until the 8th iteration, below that it resembles the lower bi-Kenyons
%C Level 6 bi-Kenyon substitution sequence.
%H Richard Kenyon, <a href="http://arXiv.org/abs/math.MG/9505210">The Construction of Self-Similar Tilings</a>
%t 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 Cf. A000120, A073058.
%K nonn,tabf
%O 0,3
%A _Roger L. Bagula_, Apr 05 2005
|
