Find the recurrence relation and initial conditions for the number of ways to tile a road of length $n$ cm, using blue, red and green tiles such that the length of each blue tile is 2 cm, green one is 1 cm, red one is 3 cm, and green & blue tiles must not be adjacent.
Hey all. So I defined $a_n$- The requested solution. $b_n$- number of ways such that the first tile is not blue. $c_n$- number of ways such that the first tile is not green. I would like to find the recurrence relation using these definitions, but am quite clueless on how to continue from here. Thanks in advance :)