Geodesic
An improved lower bound on the number of ternary squarefree words
Journal of integer sequences, Tome 19 (2016) no. 6
Let $s_{n}$ be the number of words in the ternary alphabet $\Sigma = {0, 1, 2}$ such that no subword (or factor) is a square (a word concatenated with itself, e.g., 11, 1212, and 102102). From computational evidence, the sequence $(s_{n})$ grows exponentially at a rate of about $1.317277^{n}$. While known upper bounds are already relatively close to the conjectured rate, effective lower bounds are much more difficult to obtain. In this paper, we construct a 54-Brinkhuis 952-triple, which leads to an improved lower bound on the number of $n$-letter ternary squarefree words: $952^{n/53}$ ≈ $1.1381531^{n}$.
Classification : 57M15, 11Y55 
@article{JIS_2016__19_6_a5,
     author = {Sollami,  Michael and Douglas,  Craig C. and Liebmann,  Manfred},
     title = {An improved lower bound on the number of ternary squarefree words},
     journal = {Journal of integer sequences},
     year = {2016},
     volume = {19},
     number = {6},
     zbl = {1345.05004},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2016__19_6_a5/}
}
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%A Liebmann,  Manfred
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Sollami,  Michael; Douglas,  Craig C.; Liebmann,  Manfred. An improved lower bound on the number of ternary squarefree words. Journal of integer sequences, Tome 19 (2016) no. 6. http://geodesic.mathdoc.fr/item/JIS_2016__19_6_a5/