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n-series

Source: China South East Mathematicall Olympiad Grade 10 Prob.3

July 30, 2016
combinatorics

Problem Statement

Given any integer n≥3n\geq 3. A finite series is called nn-series if it satisfies the following two conditions 1)1) It has at least 33 terms and each term of it belongs to {1,2,...,n}\{ 1,2,...,n\} 2)2) If series has mm terms a1,a2,...,ama_1,a_2,...,a_m then (ak+1−ak)(ak+2−ak)<0(a_{k+1}-a_k)(a_{k+2}-a_k)<0 for all k=1,2,...,m−2k=1,2,...,m-2
How many nn-series are there ??
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