Abstract:Zeckendorf's Theorem states that every positive integer can be uniquely represented as a sum of non-adjacent Fibonacci numbers, indexed from 1, 2, 3, 5, . . .. This has been generalized by many authors, in particular to constant coefficient fixed depth linear recurrences with positive (or in some cases non-negative) coefficients. In this work we extend this result to a recurrence with non-constant coefficients, an+1 = nan + an−1. The decomposition law becomes every m has a unique decomposition as siai with si … Show more
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