A Huffman code for 3 symbols consists of the codewords 0, 10, and 11. Find the number of binary strings of length n that are valid encodings with these codewords. Specifically, find the number of distinct strings of length n that can be obtained by concatenating copies of the strings 0, 10 and 11. For example, 0101110 is a valid string (0 10 11 10) but 1100101 is not. You may assume that n is even.