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TOT 200 1988 Autumn S3 rearrangements of 1 , 2,..., n

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March 7, 2021
permutationscombinatorics

Problem Statement

The integers 1,2,...,n1 , 2,..., n are rearranged in such a way that if the integer k,1≤k≤nk, 1 \le k\le n, is not the first term, then one of the integers k+1k + 1 or k−1k-1 occurs to the left of kk . How many arrangements of the integers 1,2,...,n1 , 2,..., n satisfy this condition?
(A. Andjans, Riga)
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