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Recurrence and permutations.

Source:

September 29, 2010
combinatoricscountingrecurrence relationpermutationsIMO ShortlistIMO Longlist

Problem Statement

(GDR3)(GDR 3) Find the number of permutations a1,⋯ ,ana_1, \cdots, a_n of the set {1,2,...,n}\{1, 2, . . ., n\} such that ∣ai−ai+1∣≠1|a_i - a_{i+1}| \neq 1 for all i=1,2,...,n−1.i = 1, 2, . . ., n - 1. Find a recurrence formula and evaluate the number of such permutations for n≤6.n \le 6.
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