\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
Find the dimension of the \(\mathbb{R}\)-vector space of sequences \((u_n)\) satisfying \(u_{n+2} = u_{n+1} + u_n\) for all \(n \in \mathbb{N}\) (Fibonacci). Give an explicit basis.
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