A324772 The "Octanacci" sequence: Trajectory of 0 under the morphism 0->{0,1,0}, 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, 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, 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, 0, 0, 1, 0, 0, 1, 0, 0

Offset

0

Comments

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

Used to construct the "labyrinth" tiling.

The binary complement, trajectory of 1 under the morphism 0->1, 1->101, is given by A104521. - Michel Dekking, Sep 04 2022

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..8118

M. Baake and R. V. Moody, Self-Similar Measures for Quasicrystals, 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.

Clément Sire, Rémy Mosseri, and Jean-François Sadoc, Geometric study of a 2D tiling related to the octagonal quasiperiodic tiling, Journal de Physique 50.24 (1989): 3463-3476. See Eq. 2; HAL Id : jpa-00211156.

Index entries for sequences that are fixed points of mappings

Maple

f(0):= (0, 1, 0): f(1):= (0): #A324772 A:= [0]:
for i from 1 to 6 do A:= map(f, A) od:
A;

Mathematica

Nest[Function[l, Flatten[l/.{0->{0, 1, 0}, 1->{0}}]], {1}, 6] (* Vincenzo Librandi, Mar 14 2019 *)

Crossrefs

See A106035 for version over {1,2}.

Sequence in context: A324964 A285957 A292273 * A285949 A285530 A317542

Adjacent sequences: A324769 A324770 A324771 * A324773 A324774 A324775

Keyword

nonn

Author

N. J. A. Sloane, Mar 13 2019

Status

approved