Each day Angela eats lunch at a deli, ordering one of the following: chicken salad, a tuna sandwich, or a turkey wrap. Find a recurrence relation for the number of ways for her to order lunch for the $n$ days if she never orders chicken salad three days in a row.
I found a solution here: https://answers.yahoo.com/question/index?qid=20080518143728AAmAnM5
I am trying to understand it.
For $n=5$, why are there $6$ choices for aaa-- and --aaa?
I have:
aaabb, aaacc, aaabc, aaacb
Where do the other two possibilities come from?