Fibonacci polynomial

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Fibonacci polynomials are defined by $$F_n(x)=\left\{ \begin{array}{ll} 0&; n=0 \\ 1&; n=1 \\ xF_{n-1}(x)+F_{n-2}(x)&; n\geq 2. \end{array} \right.$$ Note the similarity with the Lucas polynomials.