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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),... 1

%I

%S 1,1,2,1,2,2,3,1,2,2,3,2,3,3,4,1,2,2,3,2,3,3,4,2,3,3,4,3,4,4,4,4,7,5,

%T 1,2,2,3,2,3,3,4,2,3,3,4,3,4,4,4,4,7,5,2,3,3,4,3,4,4,4,4,7,5,3,4,4,4,

%U 4,7,5,4,4,4,7,5,4,4,7,5,4,4,7,5,4,4,7,5,8,6,1,2,2,3,2,3,3,4,2,3,3,4,3,4,4

%N 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 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 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 -> {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 Cf. A000120, A073058.

%K nonn,tabf

%O 0,3

%A _Roger L. Bagula_, Apr 04 2005

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Last modified March 28 20:01 EDT 2020. Contains 333103 sequences. (Running on oeis4.)