Abstract
AbstractIn the present study, we show that the second-order nonlinear difference equation $$\begin{aligned} x_{n}=\frac{x_{n-1}x_{n-2}-a}{x_{n-1}-x_{n-2}},\ n\in \mathbb {N}_{0}, \end{aligned}$$
x
n
=
x
n
-
1
x
n
-
2
-
a
x
n
-
1
-
x
n
-
2
,
n
∈
N
0
,
where $$a\in \left[ 0,\infty \right) $$
a
∈
0
,
∞
and the initial values $$x_{-2}$$
x
-
2
, $$x_{-1}$$
x
-
1
are real numbers, is solvable in closed form and that solutions can be analyzed in detail by the Fibonacci numbers.
Funder
Nevsehir Haci Bektas Veli University
Publisher
Springer Science and Business Media LLC