On the Rational Recursive Sequence xn+1 = Axn + Bxn-k + beta xn+gamma x(n-k)/Cxn+Dxn-k

In this article, we study the global and asymptotic properties of the solutions of the difference equation x(n+1) = Ax(n) +Bx(n-k) + (beta x(n) + gamma x(n-k))/(Cx(n) + Dx(n-k)), n = 0, 1, 2, ... , where the initial conditions x(-k), ... , x(-1), x(0) are arbitrary positive real numbers and the coefficients A, B, C, D, beta and gamma are positive constants, while k is a positive integer number. Some numerical examples will be given to illustrate our results.