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Zeckendorf proved any integer can be decomposed uniquely as a sum of non-adjacent Fibonacci numbers, Fn. Using continued fractions, Lekkerkerker proved the average number of summands of an m∈[Fn,Fn+1) is essentially n/(φ2+1), with φ the golden ratio. This result has been generalized by many, often using Markov processes, to show that for any positive linear recurrence the number of summands in decompositions...
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