Further Examples: Fibonacci

Here is a list of the first few Fibonacci numbers.

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Here is the th Fibonacci number.

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The limit as of the ratio of successive Fibonacci numbers is GoldenRatio.

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Here are some identities involving Fibonacci numbers.

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Here are some simplifications involving Fibonacci numbers.

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You can use FunctionExpand to expand expressions involving Fibonacci numbers.

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You can get rid of the Cos with Simplify.

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Here is a similar example for Fibonacci polynomials.

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The defined function LeadingIndex gives the largest integer k such that Fibonacci[k] does not exceed n.

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Every non-negative integer can be written uniquely as a sum of Fibonacci numbers no two consecutive. The defined function ZeckendorfRepresentation gives the coefficients of this expansion descending from the leading index.

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Here is the Zeckendorf representation of .

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The defined function ff gives the Fibonacci numbers corresponding to the Zeckendorf representation r.

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