Representation of solutions of bilinear difference equations in terms of generalized Fibonacci sequences

Abstract

Well-defined solutions of the bilinear difference equation are represented in terms of generalized Fibonacci sequences and the initial value. Our results extend and give natural explanations of some recent results in the literature. Some applications concerning a two-dimensional system of bilinear difference equations are also given.

Keywords

• bilinear difference equation
• solvable difference equation
• generalized fibonacci sequence