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Integers with a maximal number of Fibonacci representations

Petra Kocábová; Zuzana Masáková; Edita Pelantová — 2005

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

We study the properties of the function $R (n)$ which determines the number of representations of an integer $n$ as a sum of distinct Fibonacci numbers $F_{k}$ . We determine the maximum and mean values of $R (n)$ for $F_{k} \leq n < F_{k + 1}$ .

Integers with a maximal number of Fibonacci representations

Petra Kocábová; Zuzana Masáková; Edita Pelantová — 2010

RAIRO - Theoretical Informatics and Applications

We study the properties of the function which determines the number of representations of an integer as a sum of distinct Fibonacci numbers . We determine the maximum and mean values of for .

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