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A note on Fibonacci numbers of even index. (English) Zbl 1444.11031

Summary: We introduce a representation of the integers based only on Fibonacci numbers of odd index. Then we give an elementary combinatorial proof of the fact that a positive integer \(n\) is a Fibonacci number of even index if and only if \(\langle n\varphi\rangle+\frac{1}{n}>1\).

MSC:

11B39 Fibonacci and Lucas numbers and polynomials and generalizations
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Online Encyclopedia of Integer Sequences:

F(2n) = bisection of Fibonacci sequence: a(n) = 3*a(n-1) - a(n-2).

References:

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