Abstract
In this paper we study the behavior of the difference equation
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$$x_{n + 1} = ax_{n - 2} + \frac{{bx_n x_{n - 2} }}{{cx_n + dx_{n - 3} }},n = 0,1,...$$
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where the initial conditions
x
−3
,
x
−2
,
x
−1
,
x
0
are arbitrary positive real numbers and
a, b, c, d
are positive constants. Also, we give the solution of some special cases of this equation.