RAIRO - Theoretical Informatics and Applications

Research Article

Integers with a maximal number of Fibonacci representations

Petra Kocábováa1, Zuzana Masákováa1 and Edita Pelantováa1

a1 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

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 F k . We determine the maximum and mean values of R(n) for Fk ≤ n < Fk+1 .

(Received February 17 2004)

(Accepted June 8 2004)

(Online publication April 15 2005)

Key Words:

  • Fibonacci numbers;
  • Zeckendorf representation.

Mathematics Subject Classification:

  • 11A67;
  • 11B39
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