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Issue RAIRO-Theor. Inf. Appl.
Volume 39, Number 2, April-June 2005
Page(s) 343 - 359
DOI 10.1051/ita:2005022

Theoret. Informatics Appl. 39, 343-359 (2005)
DOI: 10.1051/ita:2005022

Integers with a maximal number of Fibonacci representations

Petra Kocábová, Zuzana Masáková and Edita Pelantová

Department of Mathematics, FNSPE, Czech Technical University, Trojanova 13, 120 00 Praha 2, Czech Republic; petra.kocabova@centrum.cz, masakova@km1.fjfi.cvut.cz, pelantova@km1.fjfi.cvut.cz


(Received February 17, 2004. Accepted June 8, 2004.)

Abstract
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 Fk. We determine the maximum and mean values of R(n) for $F_k\leq n<F_{k+1}$.


Mathematics Subject Classification. 11A67, 11B39

Key words: Fibonacci numbers -- Zeckendorf representation.


© EDP Sciences 2005


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