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A254990 4-bonacci word. Fixed point of morphism 0->01, 1->02, 2->03, 3->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, 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 (list; graph; refs; listen; history; text; internal format)
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

Table of n, a(n) for n=0..107.

F. Michel Dekking, Morphisms, Symbolic Sequences, and Their Standard Forms, Journal of Integer Sequences, Vol. 19 (2016), Article 16.1.1.

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).

Sequence in context: A162590 A276424 A191258 * A191255 A007814 A265330

Adjacent sequences:  A254987 A254988 A254989 * A254991 A254992 A254993

KEYWORD

nonn,easy

AUTHOR

Ondrej Turek, Feb 11 2015

STATUS

approved

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Last modified February 23 11:41 EST 2018. Contains 299579 sequences. (Running on oeis4.)