A105105 Triangle read by rows, based on the morphism f: 1-> 2->3 3->{6,5,4} 4->5 5->6 6->{3,2,1}. 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, 6, 5, 4, 1, 2, 2, 3, 2, 3, 3, 6, 5, 4, 2, 3, 3, 6, 5, 4, 3, 6, 5, 4, 6, 5, 4, 3, 2, 1, 6, 5, 1, 2, 2, 3, 2, 3, 3, 6, 5, 4, 2, 3, 3, 6, 5, 4, 3, 6, 5, 4, 6, 5, 4, 3, 2, 1, 6, 5, 2, 3, 3, 6, 5, 4, 3, 6, 5, 4, 6, 5, 4, 3, 2, 1, 6, 5, 3, 6, 5, 4, 6, 5, 4, 3, 2, 1, 6, 5, 6, 5

Offset

0,3

Comments

Six-symbol substitution of the bi-Kenyon type.

Links

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

Richard Kenyon, The Construction of Self-Similar Tilings

Example

Triangle begins:
1,
1, 2,
1, 2, 2, 3,
1, 2, 2, 3, 2, 3, 3, 6, 5, 4,
1, 2, 2, 3, 2, 3, 3, 6, 5, 4, 2, 3, 3, 6, 5, 4, 3, 6, 5, 4, 6, 5, 4, 3, 2, 1, 6, 5,
...

Mathematica

s[n_] := n /. {1 -> 2, 2 -> 3, 3 -> {6, 5, 4}, 4 -> 5, 5 -> 6, 6 -> {3, 2, 1}}; t[a_] := Join[a, Flatten[s /@ a]]; Flatten[ NestList[t, {1}, 5]]
NestList[ Flatten[ Join[ #, # /. {1 -> {2}, 2 ->{3}, 3 ->{6, 5, 4}, 4 ->{5}, 5-> {6}, 6-> {3, 2, 1}} ]] &, {1}, 5] // Flatten (* Robert G. Wilson v, Jun 05 2014 *)

Crossrefs

Cf. A103684.

Sequence in context: A105062 A106487 A105102 * A178677 A366888 A243924

Adjacent sequences: A105102 A105103 A105104 * A105106 A105107 A105108

Keyword

nonn,tabf

Author

Roger L. Bagula, Apr 07 2005

Status

approved