A216190 Abelian complexity function of tribonacci word (A080843).

3, 3, 4, 3, 4, 4, 4, 3, 4, 4, 4, 4, 4, 4, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 4, 5, 5, 4, 4, 4, 4, 4, 5, 5, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 4, 4, 5, 4, 5, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 4, 5, 4, 4, 4, 5, 5, 4, 4, 4, 4, 4, 5, 5, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 4, 4, 4

Offset: 1

Author

Nathan Fox, Mar 11 2013

Keywords

• nonn
• easy

Comments

For all n, a(n) equals 3,4,5,6, or 7.

The values 3,4,5,6, and 7 are all obtained infinitely often.

The first 6 occurs when n=342. The first 7 occurs when n=3914.

References

• G. Richomme, K. Saari, L. Q. Zamboni, Balance and Abelian Complexity of the Tribonacci word, Adv. Appl. Math. 45 (2010) 212-231.

Links

• F. Michel Dekking, Morphisms, Symbolic Sequences, and Their Standard Forms, Journal of Integer Sequences, Vol. 19 (2016), Article 16.1.1.
• Nathan Fox, Python code to generate sequence
• Ondrej Turek, Abelian complexity and Abelian co-decomposition, arXiv 1201:2109, Jan. 11, 2012.
• O. Turek, Abelian Complexity Function of the Tribonacci Word, J. Int. Seq. 18 (2015) # 15.3.4

Crossrefs

Cf. A080843.