# Permutations of 15

Probability Level 4

How many permutations $\sigma$ of the set $\{1, 2, \ldots, 15\}$ are there such that $\sigma (1) = 1, \lvert \sigma (n) - \sigma (n-1) \rvert \leq 2$ for $2 \leq n \leq 15$?

Details and assumptions

$\sigma(n)$ denotes the $n^{th}$ position of the permutation.

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