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, 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, 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, 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

Offset: 0

Author

Roger L. Bagula, Apr 04 2005

Keywords

• nonn
• tabf

Comments

This sequence is the next level of substitution suggested in section 6 of the Kenyon paper. A tile exists at this level as well.

Links

• Richard Kenyon, The Construction of Self-Similar Tilings

Crossrefs

Cf. A000120, A073058.

Programs

Mathematica

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]]