A105141 Triangle read by rows, based on the morphism f: 1->{1,2,1}, 2->{2,3,2}, 3->{3,1,3}. 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, 1, 2, 1, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 2, 3, 2, 1, 2, 1, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 2, 3, 2, 1, 2, 1, 1, 2, 1, 1, 2, 1, 2, 3, 2, 1, 2, 1, 1, 2, 1, 2, 3, 2, 1, 2, 1, 1, 2, 1, 2, 3, 2, 1, 2, 1, 2, 3, 2, 3, 1, 3, 2, 3, 2, 1, 2, 1, 2, 3, 2, 1, 2, 1, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 2, 3, 2, 1, 2, 1, 1, 2, 1, 1

Offset: 0

Author

Roger L. Bagula, Apr 09 2005

Keywords

• nonn
• tabf

Comments

3-symbol substitution tile called both ter dragon and fudge flake. This tile is the classic cyclotomic n=3.

Row n contains (3^(n+1)-1)/2 symbols.

Links

• F. M. Dekking, Recurrent sets, Advances in Mathematics, vol. 44, no. 1 (1982), 78-104; page 96, section 4.10.

Crossrefs

Cf. A073058, A105202, A105203.

Programs

Mathematica

s[n_] := n /. {1 -> {1, 2, 1}, 2 -> {2, 3, 2}, 3 -> {3, 1, 3}}; t[a_] := Join[a, Flatten[s /@ a]]; Flatten[ NestList[t, {1}, 4]]