### Unbounded discrepancy in Frobenius numbers.

Shallit, Jeffrey, Stankewicz, James (2011)

Integers

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Shallit, Jeffrey, Stankewicz, James (2011)

Integers

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Jean Berstel (2001)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

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We give a partial answer to a question of Carlitz asking for a closed formula for the number of distinct representations of an integer in the Fibonacci base.

Jean Berstel (2010)

RAIRO - Theoretical Informatics and Applications

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Borwein, Jonathan, Choi, Kwok-Kwong Stephen (2000)

Experimental Mathematics

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Petra Kocábová, Zuzana Masáková, Edita Pelantová (2005)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

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We study the properties of the function $R\left(n\right)$ 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 $R\left(n\right)$ for ${F}_{k}\le n\<{F}_{k+1}$.

Dobrev, V. K., Moylan, P.

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