An explicit formula and forbidden set for a higher order difference equation

In this paper, we determine the forbidden set, introduce an explicit formula for the solutions and discuss the global behavior of solutions of the difference equation x n + 1 = a x n x n - k + 1 b x n - k + 1 + c x n - k , n = 0 , 1 , … , where a , b , c are positive real numbers, the initial conditions x - k , x - k + 1 , … , x - 1 , x 0 are real numbers and k is a positive integer.