Counting Palindromic Binary Strings Without r-Runs of Ones
M. A. Nyblom
School of Mathematics and Geospatial Science
RMIT University
Melbourne, Victoria 3001
Australia
Abstract:
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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