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

0,4

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

Table of n, a(n) for n=0..104.

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

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]]

Crossrefs

Cf. A073058, A105202, A105203.

Sequence in context: A106035 A293811 A362228 * A103961 A012257 A220464

Adjacent sequences: A105138 A105139 A105140 * A105142 A105143 A105144

Keyword

nonn,tabf

Author

Roger L. Bagula, Apr 09 2005

Status

approved