A Smooth Tight Upper Bound for the Fibonacci Representation Function R(n)
Paul K. Stockmeyer · The Fibonacci Quarterly · 2008
The function R(n) that counts the number of representations of the integer n as the sum of distinct Fibonacci numbers has been studied for over 40 years, and many fascinating properties have been discovered. In this paper we prove that R(n) ≤ √ n + 1 for all n ≥ 0, with equality if and only if n = F2m − 1 for some integer m ≥ 2.