Algebraic Relations for Recursive Sequences

Through the following, we establish the conditions which allow us to express recursive sequences of real numbers, enumerated through the recurrence relation an+1 = Aan + Ban−1, by means of algebraic equations in two variables of degree n ∈ N . We do this, as far as we know, like it has never been formalized before. I’d like to precise that the work was develop without the support of any well-know results about difference equations. Recently I discover that the present work has been treated already, but in a different context, at least in the two books [Car] and [Ela]. Never the less, I found it is a good idea to publish it. It would be a simple and ready-to-use instrument to they aren’t familiar with difference equations.