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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