MathNet 2016-part-01 — 184 problems (EN–VI) Question 11

Let $n \ge 3$ an integer. Find the number of arrangements $a_1, a_2, ..., a_n$ of $1, 2, ..., n$ around a circle, in clockwise direction, such that $|a_1 - a_2| + |a_2 - a_3| + \dots + |a_{n-1} - a_n| + |a_n - a_1| = 2n - 2$.