Relations between Generalized Bi-Periodic Fibonacci and Lucas Sequences

Younseok Choo
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Younseok Choo: Department of Electronic and Electrical Convergence Engineering, Hongik University, Sejong-Ro 2639, Sejong 30016, Korea

Mathematics, 2020, vol. 8, issue 9, 1-10

Abstract: In this paper we consider a generalized bi-periodic Fibonacci { f n } and a generalized bi-periodic Lucas sequence { q n } which are respectively defined by f 0 = 0 , f 1 = 1 , f n = a f n − 1 + c f n − 2 ( n is even) or f n = b f n − 1 + c f n − 2 ( n is odd), and q 0 = 2 d , q 1 = a d , q n = b q n − 1 + c q n − 2 ( n is even) or q n = a f n − 1 + c q n − 2 ( n is odd). We obtain various relations between these two sequences.

Keywords: generalized bi-periodic Fibonacci sequence; generalized bi-periodic Lucas sequence; Binet’s formula (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (1)

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