Abstract
In this paper we study the qualitative properties and the periodic nature of the solutions of the difference equation x n + 1 = alpha x n - 2 + beta x n - 2 2 gamma x n - 2 + delta x n - 5 , n = 0 , 1 , . . . , where the initial conditions x - 5 , x - 4 , x - 3 , x - 2 , x - 1 , x 0 are arbitrary positive real numbers and alpha , beta , gamma , delta are positive constants. In addition, we derive the form of the solutions of some special cases of this equation.