Permutations of 15

Probability Level 4

How many permutations σ\sigma of the set {1,2,,15} \{1, 2, \ldots, 15\} are there such that σ(1)=1,σ(n)σ(n1)2 \sigma (1) = 1, \lvert \sigma (n) - \sigma (n-1) \rvert \leq 2 for 2n15 2 \leq n \leq 15 ?

Details and assumptions

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

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