Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

On certain Fibonacci representations

Kálmán Liptai, László Németh, Tamás Szakács, László Szalay

Abstract

One of the most popular and studied recursive series is the Fibonacci sequence. It is challenging to see how Fibonacci numbers can be used to generate other recursive sequences. In our article, we describe some families of integer recurrence sequences as rational polynomial linear combinations of Fibonacci numbers.

On certain Fibonacci representations

Abstract

One of the most popular and studied recursive series is the Fibonacci sequence. It is challenging to see how Fibonacci numbers can be used to generate other recursive sequences. In our article, we describe some families of integer recurrence sequences as rational polynomial linear combinations of Fibonacci numbers.
Paper Structure (8 sections, 4 theorems, 47 equations)

This paper contains 8 sections, 4 theorems, 47 equations.

Table of Contents

  1. Introduction
  2. Main results
  3. General approach
  4. Specific cases with equal degrees
  5. Case $s=2$, $j_1=0$, $j_2=1$, $d_1=d_2=1$
  6. Case $s=2$, $j_1=0$, $j_2=1$, $d_1=d_2=2$
  7. A particular case with non-equal degrees: $s=2$, $j_1=0$, $j_2=1$, $d_1=2$, $d_2=1$
  8. A modified problem

Key Result

Theorem 1

The terms form an integer sequence $(w_n)$ if and only if $d$ is integer and where $z_1,z_2,z_3$ are integers, too.

Theorems & Definitions (5)

  • Remark 1
  • Theorem 1
  • Theorem 2
  • Theorem 3
  • Theorem 4