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

0,4

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).

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

Example

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

Mathematica

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

Crossrefs

Cf. A000078 (lengths of iterations).

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

Cf. A316837, A316838, A316839, A316840.

Sequence in context: A276424 A346070 A191258 * A191255 A007814 A265330

Adjacent sequences: A254987 A254988 A254989 * A254991 A254992 A254993

Keyword

nonn,easy

Author

Ondrej Turek, Feb 11 2015

Status

approved