Some basic properties of the generalized bi-periodic Fibonacci and Lucas sequences

Elif Tan, Ho Hon Leung

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)

Abstract

In this paper, we consider a generalization of Horadam sequence { wn} which is defined by the recurrence relation wn= χ(n) wn 1+ cwn 2, where χ(n) = a if n is even, χ(n) = b if n is odd with arbitrary initial conditions w, w1 and nonzero real numbers a, b and c. As a special case, by taking the initial conditions 0, 1 and 2, b we define the sequences { un} and { vn} , respectively. The main purpose of this study is to derive some basic properties of the sequences { un} , { vn} and { wn} by using a matrix approach.

Original languageEnglish
Article number26
JournalAdvances in Difference Equations
Volume2020
Issue number1
DOIs
Publication statusPublished - Dec 1 2020

Keywords

  • Bi-periodic Fibonacci sequence
  • Horadam sequence
  • Matrix method

ASJC Scopus subject areas

  • Analysis
  • Algebra and Number Theory
  • Applied Mathematics

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