Fibonacci Proof (Modelling/Abstract Question)
A certain parking meter will accept only $1 or $2 coins (we're Australian... it's okay!). Parking in this regulated areas costs $1 per hour and a maximum time of six hours of parking is allowable. Coins can only be inserted into the meter one at a time, and a sequence of, say $1 + $2 is considered to be a different sequence to $2 + $1.
Determine the total number of combinations of $1 and $2 coins that are possible when payment is made for up to the maximum of 6 hours.
I have the combinations (there really aren't many) but this is under Fibonacci proofs and induction and I just can't see how's it relates? Just a couple of hints would be amazing. Please and Thanks guys :)