Question 11: What is the value of f(6)?

There is a row of n chairs and two types of people attending a party: C for chess players and S for comedians. You want to assign one person to each seat but you can never seat two chess players together or they will start talking about strategy and everyone else in the room will get bored. For example, if n = 3, the following are some valid seating arrangements: SSS, CSC, and SSC. However, the following is an invalid seating: CCS. Let f(n) denote the number of valid seating arrangements when n chairs are available.
Note that f(1) = 2, since both S and C count as valid seating arrangements; while f(2) = 3, since SS, SC, CS are valid seating arrangements but CC is not. Note that we do not need to count the arrangement SS more than once to account for the actual people seated swapping places, we are only interested in the “form” of the seating arrangement. Based on this, you can check that of the eight possible seating arrangements of three chairs, we have five that are valid: CSC, SSC, SSS, SCS, CSS, so f(3) = 5.
Based on the above data, answer the given subquestions.

What is the value of f(6)?