Recounting the sums of cubes of Fibonacci numbers (Q2883383)
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scientific article; zbMATH DE number 6032393
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Recounting the sums of cubes of Fibonacci numbers |
scientific article; zbMATH DE number 6032393 |
Statements
10 May 2012
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Recounting the sums of cubes of Fibonacci numbers (English)
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Let \(\{F_i \}_{i \geq 1}\) be a Fibonacci sequence and let \(f_n = F_{n+1}.\) A simple combinatorial proof of the identity NEWLINE\[NEWLINE\sum_{k=0}^n f_k^3 = \frac{f_{3n+4}+(-1)^n6f_{n-1}+5}{10}NEWLINE\]NEWLINE is given, and some of its applications are discussed.
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