Bi-Periodic (p,q)-Fibonacci and Bi-Periodic (p,q)-Lucas Sequences

Authors : Yasemin TAŞYURDU, Naime Şeyda TÜRKOĞLU

Pages : 1-13

Doi:10.16984/saufenbilder.1148618

View : 25 | Download : 12

Publication Date : 2023-02-28

Article Type : Research Paper

Abstract :In this paper, we define bi-periodic insert ignore into journalissuearticles values(p,q);-Fibonacci and bi-periodic insert ignore into journalissuearticles values(p,q);-Lucas sequences, which generalize Fibonacci type, Lucas type, bi-periodic Fibonacci type and bi-periodic Lucas type sequences, using recurrence relations of insert ignore into journalissuearticles values(p,q);-Fibonacci and insert ignore into journalissuearticles values(p,q);-Lucas sequences. Generating functions and Binet formulas that allow us to calculate the nth terms of these sequences are given and the convergence properties of their consecutive terms are examined. Also, we prove some fundamental identities of bi-periodic insert ignore into journalissuearticles values(p,q);-Fibonacci and bi-periodic insert ignore into journalissuearticles values(p,q);-Lucas sequences conform to the well-known properties of Fibonacci and Lucas sequences.
Keywords : Bi periodic Fibonacci Numbers, Fibonacci Number, Generalized Fibonacci Numbers, Bi periodic Lucas Numbers, Lucas Number