9. Suppose we have a sequence of n coins of amounts ci, C2, ...,cn, and we wish to choose a subset of maximal sum where the coins in the subset must have gaps of size at least two between them (as opposed to gaps of size one which we did in class). Let F(k) as usual denote the maximal amount that can be taken from the coins 1, 2, ...,k with this restriction. (a) Determine a recurrnce relation for F(k), 0