Hello, I'm having trouble trying to solve this question. Especially with (1), I'm not exactly sure how I can relate each term with recurrence relation and explain using the tile designs. I believe I'll be able to solve the rest of the question once I get it. Here's the question:
Let a{n} (n is the subscript here) be the number of 1 x n tile designs you can make using 1 x 1 squares available in 4 colors and 1 x 2 dominoes available in 5 colors.

First, find a recurrence relation to describe the problem. Explain why the recurrence relation is correct (your explanation should reference the designs of squares of dominoes)

Write out the first 6 terms of the sequence a1, a2,... . Hint: since you have a recurrence relation, the only difficult part will be finding the first two terms, which are simple counting questions

Solve the recurrence relation.
I could be wrong but I think the sequence is- a1 = 4, a2 = 4*4 + 5, a3 = 4*4*4 + 4*5, a4 = 4*4*4*4 + 4*4*5 + 5*5,...

For example, a3 = using only 1 x 1 square OR using one 1 x 1 square AND using one 1 x 2 domino.