The Zeckendorf representation of a positive integer is the unique expression of this integer as the sum of distinct Fibonacci numbers, where no two of these Fibonacci numbers are consecutive terms in the Fibonacci sequence and where the term f1 = 1 is not used (but the term f2 = 1 may be used).
Give a recursive definition of the Fibonacci number fn when n is a negative integer. Use your definition to find fn for n = −1, −2, −3, …, −10.
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