Restricted Binary Strings and Generalized Fibonacci Numbers

  • Antonio BerniniEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10248)


We provide some interesting relations involving k-generalized Fibonacci numbers between the set \(F_n^{(k)}\) of length n binary strings avoiding k of consecutive 0’s and the set of length n strings avoiding \(k+1\) consecutive 0’s and 1’s with some more restriction on the first and last letter, via a simple bijection. In the special case \(k=2\) a probably new interpretation of Fibonacci numbers is given.

Moreover, we describe in a combinatorial way the relation between the strings of \(F_n^{(k)}\) with an odd numbers of 1’s and the ones with an even number of 1’s.


Generalized Fibonacci numbers Restricted strings Consecutive patterns avoidance 


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© IFIP International Federation for Information Processing 2017

Authors and Affiliations

  1. 1.Dipartimento di Matematica E Informatica “U. Dini”Università degli Studi di FirenzeFlorenceItaly

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