login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A103269 Apply the tribonacci morphism 1 -> {1, 2}, 2 -> {1, 3}, 3 -> {1} n times to 1, and concatenate the resulting string. 7
1, 12, 1213, 1213121, 1213121121312, 121312112131212131211213, 12131211213121213121121312131211213121213121, 121312112131212131211213121312112131212131211213121121312121312112131213121121312 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

The number of letters in the n-th iteration is tribonacci(n+3) (that is, A000073(n+3)).

LINKS

N. J. A. Sloane, Table of n, a(n) for n = 0..10 (shortened by N. J. A. Sloane, Jan 18 2019)

Elena Barcucci, Luc Belanger and Srecko Brlek, On tribonacci sequences, Fib. Q., 42 (2004), 314-320. See T on page 315.

Julien Cassaigne, Sebastien Ferenczi, and Luca Q. Zamboni, Imbalances in Arnoux-Rauzy sequences, Annales de l'institut Fourier, 50 (2000), 1265-1276.

David Damanik and Luca Q. Zamboni, Arnoux-Rauzy Subshifts: Linear Recurrence, Powers and Palindromes, arXiv:math/0208137 [math.CO], 2002.

C. Holton and L. Q. Zamboni, Directed Graphs and Substitutions, Theory Comput. Systems, 34 (2001) 545-564

S. Ito and M. Kimura, On Rauzy fractal, Japan J. Indust. Appl. Math. 8 (1991) 461-486.

A. Messaoudi, Propriétes arithmétiques et dynamiques du fractal de Rauzy, J. Th. Nombres Bordeaux, 10 (1998) 195-224.

Gérard Rauzy, Nombres algébriques et substitutions, Bull. Soc. Math. France, 110 (1982), 147-178.

Bo Tan and Zhi-Ying Wen, Some properties of the Tribonacci sequence, European Journal of Combinatorics, 28 (2007) 1703-1719. See A_n.

Index entries for sequences that are fixed points of mappings

MATHEMATICA

FromDigits /@ NestList[ Flatten[ # /. {1 -> {1, 2}, 2 -> {1, 3}, 3 -> 1}] &, {1}, 7]

(* Second program: *)

FromDigits /@ SubstitutionSystem[{1 -> {1, 2}, 2 -> {1, 3}, 3 -> {1}}, {1}, 7] (* Jean-François Alcover, Nov 12 2018 *)

CROSSREFS

A092782 is limit of these strings.

Cf. A000073, A106748, A106749, A003842, A106750, A092782, A317196.

Sequence in context: A178529 A201642 A177090 * A317955 A033564 A301474

Adjacent sequences:  A103266 A103267 A103268 * A103270 A103271 A103272

KEYWORD

nonn

AUTHOR

Jonathan Vos Post and Robert G. Wilson v, May 16 2005

EXTENSIONS

Definition edited by N. J. A. Sloane, Aug 06 2018

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 11 22:31 EST 2019. Contains 329046 sequences. (Running on oeis4.)