2018 OIM Problems/Problem 5

Problem

Let $n$ be a positive integer. For a permutation $a_1, a_2, \cdots , a_n,$ of the numbers $1, 2, \cdots , n,$ we define

$b_k=\underset{1\le i\le k}{min}a_i+\underset{1\le j\le k}{max}a_j$

for each $k = 1, 2, \cdots , n$ . We say that the permutation $a_1, a_2, \cdots , a_n,$ , is "guadian" if the sequence $b_1, b_2, \cdots , b_n,$ , does not have two equal consecutive elements. How many guadian permutations exsit?

~translated into English by Tomas Diaz. ~orders@tomasdiaz.com

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2018 OIM Problems/Problem 5

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