Our main objective is to study some qualitative behavior of the solutions of the difference equation xn+1 = gxn−k + (axn + bxn−k) / (cxn − dxn−k), n = 0, 1, 2, ..., where the initial conditions x−k,..., x−1, x0 are arbitrary positive real numbers and the coefficients, a, b, c and d are positive constants, while k is a positive integer number.