A Fibonacci-counting proof begged by Benjamin and Quinn (Q2883417)
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scientific article; zbMATH DE number 6032423
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A Fibonacci-counting proof begged by Benjamin and Quinn |
scientific article; zbMATH DE number 6032423 |
Statements
10 May 2012
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A Fibonacci-counting proof begged by Benjamin and Quinn (English)
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A bijective proof is given here for the identity NEWLINE\[NEWLINE\sum_i\binom{2n}{i} f_{2i-\varepsilon}=5^n f_{2n-\varepsilon}, \quad (\varepsilon\in\{0,1\})NEWLINE\]NEWLINE as asked for by \textit{A. T. Benjamin} and \textit{J. J. Quinn} in their text [Proofs that really count. The art of combinatorial proof. The Dolciani Mathematical Expositions 27. Washington, DC: The Mathematical Association of America (2003; Zbl 1044.11001)].
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