Integers with a maximal number of Fibonacci representations
Department of Mathematics, FNSPE, Czech Technical University,
Trojanova 13, 120 00 Praha 2, Czech Republic; email@example.com, firstname.lastname@example.org, email@example.com
Accepted: 8 June 2004
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 Fk ≤ n < Fk+1.
Mathematics Subject Classification: 11A67 / 11B39
Key words: Fibonacci numbers / Zeckendorf representation.
© EDP Sciences, 2005