On the AB-generalized Fibonacci, Pell and Jacobsthal sequences by Hessenberg matrices

Authors

  • Mhelmar Labendia Department of Mathematics and Statistics, College of Science and Mathematics, Mindanao State University-Iligan Institute of Technology, 9200 Iligan City, Philippines
  • Michael Frondoza Department of Mathematics and Statistics, College of Science and Mathematics, Mindanao State University-Iligan Institute of Technology, 9200 Iligan City, Philippines

Keywords:

Fibonacci sequence, Pell sequence, Jacobsthal sequence, generalized Fibonacci sequence, AB- generalized Fibonacci sequence

Abstract

In this paper, we introduce the second order linear recurrence relation of the AB-generalized Fibonacci sequence {un} and give the relationships between {un} and Hessenberg permanents and determinants. Moreover, we also give representations of u2n and u2n+1. These formulas generalize the one obtained earlier by Kiliç et al. in [9].

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Published

2012-05-01

How to Cite

Labendia, M., & Frondoza, M. (2012). On the AB-generalized Fibonacci, Pell and Jacobsthal sequences by Hessenberg matrices. The Mindanawan Journal of Mathematics, 3(1), 41–51. Retrieved from https://journals.msuiit.edu.ph/tmjm/article/view/29

Issue

Vol. 3 No. 1

Section

Articles