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ARTICOLE SI NOTE DE INFORMATICA
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A note on the properties of Fibonacci trees’ leaves

Radu-Ioan Mihai 1

The Fibonacci sequence is very well-known and has many applications. In this note we
present some properties of the Fibonacci trees’ leaves, with applications in Computer Science.

1 Introduction

People are using numbers in their everyday life, even if their jobs are related to Mathematics
or not. Some of them are using numbers just as an instrument, but the researchers will try to
use them different in applications in order to help humanity to evolve.

It is known that Fibonacci numbers are a part of our life, being considered one of the most
interesting and important part of Mathematics too. They are frequently used in Algebra (see
[1]), Analysis and Geometry (see [3]) or Computer Science (especially in the Graph Theory).
One considers the recurrent sequence (F n ) n≥0 , defined by

F 0 = 0, F 1 = 1, F 2 = 1, F 3 = 2, F 4 = 3, F 5 = 5, F 6 = 8, ...,

related by
F n+2 = F n+1 + F n ,
for all n ≥ 0, called the Fibonacci Sequence (see, for instance, [5]).

There are many universe’s rules that are related to Fibonacci numbers (see [2], [6]), which
prove how important are these numbers for understanding the world we are living in.

But all these amazing researches could not be possible without the work of the French
´
mathematician Edouard Lucas, who made the Fibonacci sequence so well-known all around the
Globe.

A Fibonacci tree is a variant of a binary tree where a tree of order n (n > 1) has a left
subtree of order n − 1 and a right subtree of order n − 2 (see [7]).
the
We denote by L F n the number of the F n value leaves of the left subtree and with R F n
number of the F n value leaves of the right subtree, where F n is the n-th number in the Fibonacci
(n) the number of the F n value leaves of an n-order tree.
sequence. Also, T F n
√
Recall that φ is the Golden Ratio, i.e. φ = 1+ 5 .
2
1
Student, Faculty of Mathematics and Computer Science, University of Bucharest, rimihai2001@gmail.com,
radu.mihai4@s.unibuc.ro

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