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Relations between Generalized Bi-Periodic Fibonacci and Lucas Sequences

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  • Younseok Choo

    (Department of Electronic and Electrical Convergence Engineering, Hongik University, Sejong-Ro 2639, Sejong 30016, Korea)

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.

Suggested Citation

  • Younseok Choo, 2020. "Relations between Generalized Bi-Periodic Fibonacci and Lucas Sequences," Mathematics, MDPI, vol. 8(9), pages 1-10, September.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:9:p:1527-:d:409920
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    References listed on IDEAS

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    1. Falcón, Sergio & Plaza, Ángel, 2007. "On the Fibonacci k-numbers," Chaos, Solitons & Fractals, Elsevier, vol. 32(5), pages 1615-1624.
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    Cited by:

    1. Dongwei Guo & Wenchang Chu, 2022. "Sums of Pell/Lucas Polynomials and Fibonacci/Lucas Numbers," Mathematics, MDPI, vol. 10(15), pages 1-10, July.

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