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Hey is there any known combinatorial formula for nth fibonacci number?

(n+1)th fibonacci number is given by summation of r=0 to (round)n/2:C(n-r,r) Can someone verify the formula?Help!

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marked as duplicate by Brian M. Scott combinatorics Mar 20 '15 at 12:01

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

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Hint: Try to incorporate Binet's formula: http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/fibFormula.html

$$Fib(n) = \frac{\phi^n - \frac{(-1)^n}{\phi^n}}{\sqrt{5}}$$

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  • $\begingroup$ I need a combinatorial formula! $\endgroup$ – user220382 Mar 20 '15 at 12:01
  • $\begingroup$ Right, just that I thought I should add a hint which may help you get an answer eventually... $\endgroup$ – Kugelblitz Mar 20 '15 at 12:03