Problem

Christmas Contest - Team Round - Problem 19

Let $S$ be the set of all positive integers $n$ such that there exists a nonnegative integer $k<n-1$ such that the numbers $\binom{n}{k}$ , $\binom{n}{k+1}$ , and $\binom{n}{k+2}$ form an arithmetic sequence. Find the sum of the $10$ smallest elements in $S$ .

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Problem Tags: Counting and probability

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Category: Christmas Contest Team Round
Points: 4
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