Y by Adventure10, Mango247, and 1 other user
Prove that the number of pairs
of a permutation
of
and a subset
of
such that
![\[ \forall x\in S: \alpha(x)\not\in S\]](//latex.artofproblemsolving.com/3/b/5/3b5b87de58ac757a2eb09ddeb7989dcbd6b8270d.png)
is equal to
in which
is the Fibonacci sequence such that 





![\[ \forall x\in S: \alpha(x)\not\in S\]](http://latex.artofproblemsolving.com/3/b/5/3b5b87de58ac757a2eb09ddeb7989dcbd6b8270d.png)
is equal to



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