Solving the linear difference equation with periodic coefficients via Fibonacci sequences

The aim of this paper is to establish explicit solutions of homogeneous linear difference equations with periodic coefficients. For this purpose, we get around the problem by converting each equation of this class to an equivalent linear difference equation with constant coefficients. Second, we provide some expressions of the solutions via the combinatorial and the Binet formulas of weighted generalized Fibonacci sequences. Finally, some numerical examples and applications are proposed.