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Counting Palindromic Binary Strings Without ***r*-Runs of Ones

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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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