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Apply the tribonacci morphism 1 -> {1, 2}, 2 -> {1, 3}, 3 -> {1} n times to 1, and concatenate the resulting string.
7

%I #41 Aug 06 2024 09:40:13

%S 1,12,1213,1213121,1213121121312,121312112131212131211213,

%T 12131211213121213121121312131211213121213121,

%U 121312112131212131211213121312112131212131211213121121312121312112131213121121312

%N Apply the tribonacci morphism 1 -> {1, 2}, 2 -> {1, 3}, 3 -> {1} n times to 1, and concatenate the resulting string.

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

%H N. J. A. Sloane, <a href="/A103269/b103269.txt">Table of n, a(n) for n = 0..10</a> (shortened by _N. J. A. Sloane_, Jan 18 2019)

%H Elena Barcucci, Luc Belanger and Srecko Brlek, <a href="http://www.fq.math.ca/Papers1/42-4/quartbarcucci04_2004.pdf">On tribonacci sequences</a>, Fib. Q., 42 (2004), 314-320. See T on page 315.

%H Julien Cassaigne, Sebastien Ferenczi, and Luca Q. Zamboni, <a href="http://www.numdam.org/item?id=AIF_2000__50_4_1265_0">Imbalances in Arnoux-Rauzy sequences</a>, Annales de l'institut Fourier, 50 (2000), 1265-1276.

%H David Damanik and Luca Q. Zamboni, <a href="http://arxiv.org/abs/math/0208137">Arnoux-Rauzy Subshifts: Linear Recurrence, Powers and Palindromes</a>, arXiv:math/0208137 [math.CO], 2002.

%H C. Holton and L. Q. Zamboni, <a href="https://citeseerx.ist.psu.edu/pdf/c87e53604abd732cab6eaac7034160636ea39aa3">Directed Graphs and Substitutions</a>, Theory Comput. Systems, 34 (2001) 545-564

%H S. Ito and M. Kimura, <a href="http://dx.doi.org/10.1007/BF03167147">On Rauzy fractal</a>, Japan J. Indust. Appl. Math. 8 (1991) 461-486.

%H A. Messaoudi, <a href="http://dx.doi.org/10.5802/jtnb.223">Propriétes arithmétiques et dynamiques du fractal de Rauzy</a>, J. Th. Nombres Bordeaux, 10 (1998) 195-224.

%H Gérard Rauzy, <a href="http://www.numdam.org/item?id=BSMF_1982__110__147_0">Nombres algébriques et substitutions</a>, Bull. Soc. Math. France, 110 (1982), 147-178.

%H Bo Tan and Zhi-Ying Wen, <a href="http://dx.doi.org/10.1016/j.ejc.2006.07.007">Some properties of the Tribonacci sequence</a>, European Journal of Combinatorics, 28 (2007) 1703-1719. See A_n.

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

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

%t (* Second program: *)

%t FromDigits /@ SubstitutionSystem[{1 -> {1, 2}, 2 -> {1, 3}, 3 -> {1}}, {1}, 7] (* _Jean-François Alcover_, Nov 12 2018 *)

%Y A092782 is limit of these strings.

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

%K nonn

%O 0,2

%A _Jonathan Vos Post_ and _Robert G. Wilson v_, May 16 2005

%E Definition edited by _N. J. A. Sloane_, Aug 06 2018