induction & recursion: some collection of n sit in n consec.

alichaudhary said:

Again, a group of friends, which includes numerous engineers and non-engineers, are
gathering for a social occasion. At one point, some collection of n of the partygoers will sit in n
consecutive chairs. In this case, we always want two engineers sitting next to one another so
they will have someone to talk shop to and we always want two non-engineers sitting next to one
another. Also, each row will always begin with a non-engineer but may end with either type of
individual. Let Sn be the number of ways of seating n people in these n chairs? Construct all
possible arrangements and compute Sn for all values up to n = 5. Find and prove the correctness
of a formula for Sn.

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