On the solutions of a second-order difference equation in terms of generalized Padovan sequences
Keyword(s):
AbstractThis paper deals with the solution, stability character and asymptotic behavior of the rational difference equation$$\begin{array}{} \displaystyle x_{n+1}=\frac{\alpha x_{n-1}+\beta}{ \gamma x_{n}x_{n-1}},\qquad n \in \mathbb{N}_{0}, \end{array}$$where ℕ0= ℕ ∪ {0},α,β,γ∈ ℝ+, and the initial conditionsx–1andx0are non zero real numbers such that their solutions are associated to generalized Padovan numbers. Also, we investigate the two-dimensional case of the this equation given by$$\begin{array}{} \displaystyle x_{n+1} = \frac{\alpha x_{n-1} + \beta}{\gamma y_n x_{n-1}}, \qquad y_{n+1} = \frac{\alpha y_{n-1} +\beta}{\gamma x_n y_{n-1}} ,\qquad n\in \mathbb{N}_0. \end{array}$$
2016 ◽
Vol 2016
◽
pp. 1-14
◽
2020 ◽
Vol 27
(2)
◽
pp. 165-175
◽
2008 ◽
Vol 14
(4)
◽
pp. 429-432
◽
2003 ◽
Vol 16
(5)
◽
pp. 627-633
◽
2018 ◽
Vol 39
(16)
◽
pp. 1727-1741
1992 ◽
Vol 41
(1-2)
◽
pp. 95-103
◽