Turkish Journal of Analysis and Number Theory
ISSN (Print): 2333-1100 ISSN (Online): 2333-1232 Website: http://www.sciepub.com/journal/tjant
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Turkish Journal of Analysis and Number Theory. 2017, 5(4), 139-142
DOI: 10.12691/tjant-5-4-4
Open AccessArticle

Some Formulas for the Generalized Kolakoski Sequence Kol(a, b)

Abdallah Hammam1,

1Université Moulay Ismaïl, Faculté des sciences Département de Mathématiques et Informatique, 50020 Meknès, Morocco

Pub. Date: June 14, 2017

Cite this paper:
Abdallah Hammam. Some Formulas for the Generalized Kolakoski Sequence Kol(a, b). Turkish Journal of Analysis and Number Theory. 2017; 5(4):139-142. doi: 10.12691/tjant-5-4-4

Abstract

We present here a new approach to investigate the Kolakoski sequence Kol(a, b). In the first part of this paper, we give some general identities. In the second, we state our main result, which concerns the frequency of the letters in the case where a and b are odd. Finally, we give an algorithm to compute the term Kn in the particular case of Kol(1, 3).

Keywords:
Kolakoski sequence recursion recursive formula

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References:

[1]  M. Baake and B. Sing, Kolakoski (3,1) is a (deformed) model set, Canad. Math. Bull.47(2):168-90 (2004).
 
[2]  S. Brlek, D. Jamet and G. Paquin, Smooth words on 2-letter alphabet having same parity, Theoritical Computer Science, Elsevier, 2008, 393 (1-3), pp 166-181.
 
[3]  A. Hammam, Some new Formulas for the Kolakoski Sequence A000002. Turkish Journal of Analysis and Number Theory . 2016; 4(3):54-59.
 
[4]  W. Kolakoski, Problem 5304: Self Generating Runs, Amer. Math. Monthly 72 (1965), 674.
 
[5]  Rufus Oldenburger, Exponent trajectories in symbolic dynamics, Trans Amer. Math. Soc. 46 (1939), 453-466.
 
[6]  B. Shen, A uniformness of the Kolakoski sequence, graph, connectivity and correlations (2017) arXiv :1703.00180.
 
[7]  B. Sing, Kolakoski(2m,2n) are limit-periodic Model Sets, arXiv 0207037.
 
[8]  N. J. A. Sloane, The On-line Encyclopedia of Integer Sequences, published electronically at http://oeis.org.