HMMT 2009 C10
- Combinatorics
- Answer
Given a rearrangement of the numbers from 1 to , each pair of consecutive elements and of the sequence can be either increasing (if ) or decreasing (if ). How many rearrangements of the numbers from 1 to have exactly two increasing pairs of consecutive elements?
Dataset text NuminaMath olympiads. Quoted with source.
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3^{n}-(n+1) \cdot 2^{n}+n(n+1) / 2
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