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

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, 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, 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

Offset: 0

Author

Ondrej Turek, Feb 11 2015

Keywords

• nonn
• easy

Comments

Special case of k-bonacci word for k = 4 (see crossrefs).

The lengths of iterations S(i) are Tetranacci numbers (A000078).

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).

Examples

			The iterates are:
0
01
0102
01020103
010201030102010
01020103010201001020103010201
01020103010201001020103010201010201030102010010201030102
...
		

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..10000
• Elena Barcucci, Luc Belanger and Srecko Brlek, On tribonacci sequences, Fib. Q., 42 (2004), 314-320. See Section 4.
• F. Michel Dekking, Morphisms, Symbolic Sequences, and Their Standard Forms, Journal of Integer Sequences, Vol. 19 (2016), Article 16.1.1.
• O. Turek, Abelian Complexity Function of the Tribonacci Word, J. Int. Seq. 18 (2015) # 15.3.4

Crossrefs

Cf. A000078 (lengths of iterations).

Cf. A003849 (k=2, Fibonacci word), A080843 (k=3, Tribonacci word).

Cf. A316837, A316838, A316839, A316840.

Programs

Mathematica

Nest[Flatten[#/.{0->{0,1},1->{0,2},2->{0,3},3->0}]&,0,7] (* Harvey P. Dale, Mar 26 2015 *)