The nonrecursive version of the function for computing Fibonacci numbers uses information accumulated during computation, whereas the recursive version does not. However, it does not mean that no recursive implementation can be given that can collect the same information as the nonrecursive counterpart. In fact, such an implementation can be obtained directly from the nonrecursive version. What would it be? Consider using two functions instead of one; one would do all the work, and the other would only invoke it with the proper parameters.
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