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 a_{n+1} = Aa_n + Ba_{n-1}, by means of algebraic equations in two variables of degree n 2 N. Then we apply main results to the relations that express Fibonacci numbers, domino tillings of the graph W_4 x P_{n-1} and Pythagorean triples.