Journal of Integer Sequences, Vol. 16 (2013), Article 13.8.7

Counting Palindromic Binary Strings Without r-Runs of Ones

M. A. Nyblom
School of Mathematics and Geospatial Science
RMIT University
Melbourne, Victoria 3001


A closed-form expression is derived for the enumeration of all palindromic binary strings of length n > r having no r-runs of 1s, in terms of the r-Fibonacci sequence. A similar closed-form expression for the number of zeros contained in all such palindromic binary strings is derived in terms of the number of zeros contained in all binary strings having no r-runs of 1s.

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(Concerned with sequences A001590 A053602.)

Received June 7 2013; revised version received September 13 2013. Published in Journal of Integer Sequences, October 13 2013.

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