Counting Palindromes According to r-Runs
of Ones Using Generating Functions
Helmut Prodinger
Department of Mathematics
Stellenbosch University
7602 Stellenbosch
South Africa
Abstract:
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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