On eight solvable systems of difference equations in terms of generalized Padovan sequences

Abstract

In this study we show that the systems of difference equationsfor n ∈ N 0 , where the sequences p n , q n , r n and s n are some of the sequences x n and y n ,1, 2}, are arbitrary real numbers in D f and the parameters a, b are arbitrary complex numbers, with b ̸ = 0, can be explicitly solved in terms of generalized Padovan sequences. Some analytical examples are given to demonstrate the theoretical results.

Global Behavior of Solutions to a Higher-Dimensional System of Difference Equations with Lucas Numbers Coefficients

“…Recently, there has been a growing interest in the study of finding closed-form solutions of difference equations and systems of difference equations. Some of the forms of solutions of these equations are representable via wellknown integer sequences such as Fibonacci numbers (see, for example [26,32]), Horadam numbers (see, for example, [30,31]), Lucas numbers (see, for example [25,27,33]), Pell numbers and Padovan numbers (see, for example [34][35][36]), But in this paper, we present the solution in the form of Lucas sequences.…”