Hello! My friend gave me this interesting problem and I can't figure it out. If anyone has any ideas it would be appreciated.

Problem: Liz writes down a sequence of \(n\) letters, where each letter is A, B, or C, and the letter A appears an even number of times. How many different sequences could Liz have written down?

The answer should be in terms of n. I tried to find a recursion and a closed formed but didn't have much luck.

Guest May 28, 2021