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Open AccessArticle

by Younseok Choo

Mathematics 2020, 8(9), 1527; https://doi.org/10.3390/math8091527 - 7 Sep 2020

Cited by 5 | Viewed by 2322

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

, [...] Read more.

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. Full article

(This article belongs to the Section E1: Mathematics and Computer Science)

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