Semnan University International Journal of Nonlinear Analysis and Applications 2008-6822 13 2 2022 07 01 On a solvable system of difference equations via some number sequences 2611 2637 6724 10.22075/ijnaa.2022.26918.3451 EN Merve Kara Department of Mathematics, Kamil Ozdag Science Faculty, Karamanoglu Mehmetbey University, Karaman, Turkey Yasin Yazlik Department of Mathematics, Faculty of Science and Art, Nevsehir Haci Bektacs Veli University, Nevsehir, Turkey Journal Article 2022 04 19 In this paper, we show that the following three-dimensional rational system of difference equations<br />\begin{equation*}<br />x_{n}=\frac{z_{n-1}z_{n-3}}{bx_{n-2}+az_{n-3}}, \ y_{n}=\frac{x_{n-1}x_{n-3}}{dy_{n-2}+cx_{n-3}}, \ z_{n}=\frac{y_{n-1}y_{n-3}}{fz_{n-2}+ey_{n-3}}, \ n\in \mathbb{N}_{0},<br />\end{equation*}<br />where the parameters $a, b, c, d, e, f$\ and the initial values $x_{-i},y_{-i},z_{-i}$, $i \in \{1,2,3\}$, 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. https://ijnaa.semnan.ac.ir/article_6724_9616e5248621fd786745130077fa0e94.pdf