A082380 Number of 7/3+-power-free words over the alphabet {0,1}.

1, 2, 4, 6, 10, 14, 20, 30, 38, 50, 64, 86, 108, 136, 178, 222, 276, 330, 408, 500, 618, 774, 962, 1178, 1432, 1754, 2160, 2660, 3292

Offset: 0

Author

Ralf Stephan, Apr 10 2003

Keywords

• nonn

Links

• J. Karhumäki and J. Shallit, Polynomial vs Exponential Growth in Repetition-Free Binary Words
• A. M. Shur, Growth properties of power-free languages, Computer Science Review, Vol. 6 (2012), 187-208.
• A. M. Shur, Numerical values of the growth rates of power-free languages, arXiv:1009.4415 [cs.FL], 2010.

Crossrefs

Cf. A038952, A028445, A007777, A082379.

Formula

Let L = lim a(n)^(1/n); then L exists since a(n) is submultiplicative. 1.2206318 < L < 1.22064482 (Shur 2012); the gap between the bounds can be made less than any given constant. Empirically, the upper bound is precise: L=1.2206448... . - Arseny Shur, Apr 26 2015

Extensions

Changed name by Jeffrey Shallit, Sep 26 2014