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A254990 4-bonacci word. Fixed point of morphism 0->01, 1->02, 2->03, 3->0.

%I A254990 #25 Jan 05 2025 19:51:40
%S A254990 0,1,0,2,0,1,0,3,0,1,0,2,0,1,0,0,1,0,2,0,1,0,3,0,1,0,2,0,1,0,1,0,2,0,
%T A254990 1,0,3,0,1,0,2,0,1,0,0,1,0,2,0,1,0,3,0,1,0,2,0,1,0,2,0,1,0,3,0,1,0,2,
%U A254990 0,1,0,0,1,0,2,0,1,0,3,0,1,0,2,0,1,0,1,0,2,0,1,0,3,0,1,0,2,0,1,0,0,1,0,2,0,1,0,3
%N A254990 4-bonacci word. Fixed point of morphism 0->01, 1->02, 2->03, 3->0.
%C A254990 Special case of k-bonacci word for k = 4 (see crossrefs).
%C A254990 The lengths of iterations S(i) are Tetranacci numbers (A000078).
%C A254990 Set S(0) = 0; S(1) = 0,1; S(2) = 0,1,0,2; S(3) = 0,1,0,2,0,1,0,3; for n >= 4: S(n) = S(n-1) S(n-2) S(n-3) S(n-4). The sequence is the limit S(infinity).
%H A254990 Seiichi Manyama, <a href="/A254990/b254990.txt">Table of n, a(n) for n = 0..10000</a>
%H A254990 Elena Barcucci, Luc Belanger and Srecko Brlek, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Papers1/42-4/quartbarcucci04_2004.pdf">On tribonacci sequences</a>, Fib. Q., 42 (2004), 314-320. See Section 4.
%H A254990 F. Michel Dekking, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL19/Dekking/dekk4.html">Morphisms, Symbolic Sequences, and Their Standard Forms</a>, Journal of Integer Sequences, Vol. 19 (2016), Article 16.1.1.
%H A254990 O. Turek, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL18/Turek/turek3.html">Abelian Complexity Function of the Tribonacci Word</a>, J. Int. Seq. 18 (2015) # 15.3.4
%e A254990 The iterates are:
%e A254990 0
%e A254990 01
%e A254990 0102
%e A254990 01020103
%e A254990 010201030102010
%e A254990 01020103010201001020103010201
%e A254990 01020103010201001020103010201010201030102010010201030102
%e A254990 ...
%t A254990 Nest[Flatten[#/.{0->{0,1},1->{0,2},2->{0,3},3->0}]&,0,7] (* _Harvey P. Dale_, Mar 26 2015 *)
%Y A254990 Cf. A000078 (lengths of iterations).
%Y A254990 Cf. A003849 (k=2, Fibonacci word), A080843 (k=3, Tribonacci word).
%Y A254990 Cf. A316837, A316838, A316839, A316840.
%K A254990 nonn,easy
%O A254990 0,4
%A A254990 _Ondrej Turek_, Feb 11 2015