# Restricted Binary Strings and Generalized Fibonacci Numbers

Abstract : 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.
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https://hal.inria.fr/hal-01656354
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Submitted on : Tuesday, December 5, 2017 - 3:42:16 PM
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### Citation

Antonio Bernini. Restricted Binary Strings and Generalized Fibonacci Numbers. 23th International Workshop on Cellular Automata and Discrete Complex Systems (AUTOMATA), Jun 2017, Milan, Italy. pp.32-43, ⟨10.1007/978-3-319-58631-1_3⟩. ⟨hal-01656354⟩

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