Geodesic
Counting palindromes according to \(r\)-runs of ones using generating functions
Journal of integer sequences, Tome 17 (2014) no. 6
We derive generating functions for the enumeration of all palindromic binary strings of length $n$ having only runs of 1's of length $\le r$. We provide asymptotic expressions for fixed $r$ and $n \to \infty $. Eventually, $r$ is treated as a random variable and an asymptotic equivalent for the largest run of 1's in binary palindromes is derived.
Classification : 11B39, 05A15
Keywords: binary string, generating function, r-run of ones, asymptotics 
@article{JIS_2014__17_6_a1,
     author = {Prodinger,  Helmut},
     title = {Counting palindromes according to \(r\)-runs of ones using generating functions},
     journal = {Journal of integer sequences},
     year = {2014},
     volume = {17},
     number = {6},
     zbl = {1360.11034},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2014__17_6_a1/}
}
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%J Journal of integer sequences
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Prodinger,  Helmut. Counting palindromes according to \(r\)-runs of ones using generating functions. Journal of integer sequences, Tome 17 (2014) no. 6. http://geodesic.mathdoc.fr/item/JIS_2014__17_6_a1/