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A Fibonacci curiosity. (English)
Math. Spectr. 48, No. 1, 13-15 (2015).
Summary: Using recursion, we establish that the sums $\sum_{k\ge 0,k \text{even}}{m-k\choose k}$ and $\sum_{k\ge 0,k \text{odd}}{m-k\choose k}$, which occur in the well-known Lucas formula, are equal if and only if $m=3n-1$.
Classification: F60