%I #16 Jan 20 2017 00:01:22

%S 1,3,7,15,33,67,145

%N Length of the longest squarefree and rich word over an alphabet of n letters.

%C A squarefree and rich word over a fixed alphabet always has bounded length (see Pelantová & Starosta). A word is squarefree if it does not contain squares as subwords, and a word of length n is rich if it contains exactly n+1 distinct palindromes (including the empty word) as subwords.

%C It is known that 2.008^n <= a(n) <= 2.237^n for n >= 5 (see Vesti).

%H E. Pelantová, Š. Starosta, <a href="http://arxiv.org/abs/1103.4051">Languages invariant under more symmetries: overlapping factors versus palindromic richness</a>, arXiv:1103.4051 [math.CO], 2011-2012.

%H E. Pelantová, Š. Starosta, <a href="http://dx.doi.org/10.1016/j.disc.2013.07.002">Languages invariant under more symmetries: overlapping factors versus palindromic richness</a>, Discrete Mathematics, 313.21 (2013), 2432-2445.

%H Jetro Vesti, <a href="http://arxiv.org/abs/1603.01058">Rich square-free words</a>, arXiv:1603.01058 [math.CO], 2016.

%e For n = 3, the longest squarefree and rich words are (up to isomorphism) 0102010 and 0121012. For n = 4, e.g., the word 010201030102010 has maximal length.

%K hard,more,nonn

%O 1,2

%A _Jarkko Peltomäki_, Feb 29 2016