on a solvable system of difference equations via some number sequences

In this paper, we show that the following three-dimensional rational system of difference equations xn = zn−1zn−3/bxn−2 + azn−3, yn = xn−1xn−3/dyn−2 + cxn−3, zn = yn−1yn−3/fzn−2 + eyn−3, n ∈ n0, where the parameters a, b, c, d, e, f and the initial values x−i , y−i , z−i , i ∈ {1, 2, 3}, are real numbers, can be solved in explicit form. in addition, the solutions of aforementioned systems according to the special cases of the parameters are given in closed form. later, the forbidden set of the initial values for aforementioned system is described. finally, an application and numerical examples to support our results are given.