Journal of Integer Sequences, Vol. 17 (2014), Article 14.6.2

Counting Palindromes According to r-Runs of Ones Using Generating Functions

Helmut Prodinger
Department of Mathematics
Stellenbosch University
7602 Stellenbosch
South Africa


We derive generating functions for the enumeration of all palindromic binary strings of length n having only runs of 1's of length ≤ r. We provide asymptotic expressions for fixed r and n → ∞. Eventually, r is treated as a random variable and an asymptotic equivalent for the largest run of 1's in binary palindromes is derived.

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Received October 29 2013; revised version received April 6 2014; April 15 2014. Published in Journal of Integer Sequences, April 15 2014.

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