On the solutions of 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) = ax(n)x(n-k)/bx(n) - cx(n-k-1), n = 0, 1, ..., where a, b, c are positive real numbers and the initial conditions x(-k-1), x(-k), ..., x(-1), x(0) are real numbers. We show that when a = b = c, the behavior of the solutions depends on whether k is even or odd.