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

Creative Commons License

TAN E., Leung H.

ADVANCES IN DIFFERENCE EQUATIONS, cilt.2020, sa.1, 2020 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 2020 Sayı: 1
  • Basım Tarihi: 2020
  • Doi Numarası: 10.1186/s13662-020-2507-4
  • Dergi Adı: ADVANCES IN DIFFERENCE EQUATIONS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, Metadex, zbMATH, Directory of Open Access Journals, Civil Engineering Abstracts
  • Anahtar Kelimeler: Horadam sequence, Bi-periodic Fibonacci sequence, Matrix method, 11B39, 05A15, IDENTITIES
  • Ankara Üniversitesi Adresli: Evet

Özet

In this paper, we consider a generalization of Horadam sequence {wn} which is defined by the recurrence relation wn=chi (n)wn-1+cwn-2, where chi (n)=a if n is even, chi (n)=b if n is odd with arbitrary initial conditions w0, 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.