A106154 - OEIS

%I #24 Aug 19 2020 07:55:57

%S 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,

%T 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,

%U 4,5,4,5,6,5,6,5,4,5,6,5,6,5,4,5,4,3,4

%N 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.

%C 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.

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

%H Jinyuan Wang, <a href="/A106154/b106154.txt">Table of n, a(n) for n = 0..242</a>

%H F. M. Dekking, <a href="http://dx.doi.org/10.1016/0001-8708(82)90066-4">Recurrent Sets</a>, Advances in Mathematics, vol. 44, no.1, April 1982, page 96, section 4.11.

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

%t 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]

%t 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 *)

%Y Cf. A105969.

%K nonn,fini,full

%O 0,1

%A _Roger L. Bagula_, May 07 2005

%E New name from _Joerg Arndt_, Jun 17 2015