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Enumerating binary strings without r-runs of ones

journal contribution
posted on 2024-11-01, 11:55 authored by Michael NyblomMichael Nyblom
The number of binary strings of length n containing no substrings consisting of r consecutive ones is examined and shown to be given in terms of a well known integer sequence namely, the r-Fibonacci sequence. In addition, difference equations for the number of zeros and the total number of runs within these binary strings are derived.

History

Journal

International Mathematical Forum

Volume

7

Issue

38

Start page

1865

End page

1876

Total pages

12

Publisher

Hikari Ltd

Place published

Bulgaria

Language

English

Copyright

© 2012 Hikari Ltd

Former Identifier

2006037599

Esploro creation date

2020-06-22

Fedora creation date

2012-11-02

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