Geodesic
Binary words avoiding $xx^Rx$ and strongly unimodal sequences
Journal of integer sequences, Tome 18 (2015) no. 10.

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Summary: In previous work, Currie and Rampersad showed that the growth of the number of binary words avoiding the pattern $x x^{R} x$ was intermediate between polynomial and exponential. We now show that the same result holds for the growth of the number of binary words avoiding the pattern $x x^{R} x$ . Curiously, the analysis for $x x^{R} x$ is much simpler than that for $x x^{R} x$ . We derive our results by giving a bijection between the set of binary words avoiding $x x^{R} x$ and a class of sequences closely related to the class of "strongly unimodal sequences".
Classification : 68R15
Keywords: pattern with reversal, avoidability in words, strongly unimodal sequence 
@article{JIS_2015__18_10_a0,
     author = {Currie, James and Rampersad, Narad},
     title = {Binary words avoiding $xx^Rx$ and strongly unimodal sequences},
     journal = {Journal of integer sequences},
     publisher = {mathdoc},
     volume = {18},
     number = {10},
     year = {2015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2015__18_10_a0/}
}
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Currie, James; Rampersad, Narad. Binary words avoiding $xx^Rx$ and strongly unimodal sequences. Journal of integer sequences, Tome 18 (2015) no. 10. http://geodesic.mathdoc.fr/item/JIS_2015__18_10_a0/