A324772 - OEIS

%I #20 Sep 04 2022 09:29:42

%S 0,1,0,0,0,1,0,0,1,0,0,1,0,0,0,1,0,0,1,0,0,0,1,0,0,1,0,0,0,1,0,0,1,0,

%T 0,1,0,0,0,1,0,0,1,0,0,0,1,0,0,1,0,0,1,0,0,0,1,0,0,1,0,0,0,1,0,0,1,0,

%U 0,1,0,0,0,1,0,0,1,0,0,0,1,0,0,1,0,0,0,1,0,0,1,0,0

%N The "Octanacci" sequence: Trajectory of 0 under the morphism 0->{0,1,0}, 1->{0}.

%C The sequence is S_oo where S_0 = 1, S_1 = 0; S_{n+2} = S_{n+1} S_n S_{n+1}.

%C Used to construct the "labyrinth" tiling.

%C The binary complement, trajectory of 1 under the morphism 0->1, 1->101, is given by A104521. - _Michel Dekking_, Sep 04 2022

%H Vincenzo Librandi, <a href="/A324772/b324772.txt">Table of n, a(n) for n = 0..8118</a>

%H M. Baake and R. V. Moody, <a href="https://arxiv.org/abs/math/0008063">Self-Similar Measures for Quasicrystals</a>, in Directions in Mathematical Quasicrystals (eds. M. Baake and R. V. Moody), CRM Monograph Series, vol. 13, AMS, Providence, RI (2000), pp. 1-42; arXiv:math/0008063 [math.MG], 2000.

%H Clément Sire, Rémy Mosseri, and Jean-François Sadoc, <a href="https://hal.archives-ouvertes.fr/jpa-00211156">Geometric study of a 2D tiling related to the octagonal quasiperiodic tiling</a>, Journal de Physique 50.24 (1989): 3463-3476. See Eq. 2; HAL Id : jpa-00211156.

%H <a href="/index/Fi#FIXEDPOINTS">Index entries for sequences that are fixed points of mappings</a>

%p f(0):= (0, 1, 0): f(1):= (0): #A324772 A:= [0]:

%p for i from 1 to 6 do A:= map(f, A) od:

%p A;

%t Nest[Function[l, Flatten[l/.{0->{0, 1, 0}, 1->{0}}]], {1}, 6] (* _Vincenzo Librandi_, Mar 14 2019 *)

%Y See A106035 for version over {1,2}.

%K nonn

%O 0

%A _N. J. A. Sloane_, Mar 13 2019