A106154 Generation 5 of the substitution 1->{2, 1, 2}, 2->{3, 2, 3}, 3->{4, 3, 4}, 4->{5, 4, 5}, 5->{6, 5, 6}, 6->{1, 6, 1}, starting with 1.

6, 5, 6, 5, 4, 5, 6, 5, 6, 5, 4, 5, 4, 3, 4, 5, 4, 5, 6, 5, 6, 5, 4, 5, 6, 5, 6, 5, 4, 5, 4, 3, 4, 5, 4, 5, 4, 3, 4, 3, 2, 3, 4, 3, 4, 5, 4, 5, 4, 3, 4, 5, 4, 5, 6, 5, 6, 5, 4, 5, 6, 5, 6, 5, 4, 5, 4, 3, 4, 5, 4, 5, 6, 5, 6, 5, 4, 5, 6, 5, 6, 5, 4, 5, 4, 3, 4

Offset

0,1

Comments

Previous name was: Terdragon matrix symmetry extended to 6 symbols: characteristic polynomial: x^6 - 6*x^5 + 15*x^4 - 20*x^3 + 15*x^2 - 6*x - 63.

This sequence gives a segment of a 120-degree hexagonal border for a tile.

Links

Jinyuan Wang, Table of n, a(n) for n = 0..242

F. M. Dekking, Recurrent Sets, Advances in Mathematics, vol. 44, no.1, April 1982, page 96, section 4.11.

Formula

1->{2, 1, 2}, 2->{3, 2, 3}, 3->{4, 3, 4}, 4->{5, 4, 5}, 5->{6, 5, 6}, 6->{1, 6, 1}.

Mathematica

s[1] = {2, 1, 2}; s[2] = {3, 2, 3}; s[3] = {4, 3, 4}; s[4] = {5, 4, 5}; s[5] = {6, 5, 6}; s[6] = {1, 6, 1}; t[a_] := Flatten[s /@ a]; p[0] = {1}; p[1] = t[p[0]]; p[n_] := t[p[n - 1]]; aa = p[5]
Flatten[Nest[Flatten[#/.{1->{2, 1, 2}, 2->{3, 2, 3}, 3->{4, 3, 4}, 4->{5, 4, 5}, 5->{6, 5, 6}, 6->{1, 6, 1}} &], {5}, 7]] (* Vincenzo Librandi, Jun 17 2015 *)

Crossrefs

Cf. A105969.

Sequence in context: A064844 A242723 A111718 * A023408 A133616 A019621

Adjacent sequences: A106151 A106152 A106153 * A106155 A106156 A106157

Keyword

nonn,fini,full

Author

Roger L. Bagula, May 07 2005

Extensions

New name from Joerg Arndt, Jun 17 2015

Status

approved