I need a little bit help finding a recurrence relation. So it goes like this:
"A one-sided pavement is being made with tiles that come in 5 different colors. There are 3 light colors (light-yellow, light-green and light-red) and then there are 2 dark colors (dark-red and dark-blue). It is required that the total of tiles in light colors are an odd-number.
a) Find $a_1$ og $a_2$ b) Put forth a recurrence relation along with initial conditions for $a_n$. c) Use the recurrence relation to calculate $a_5$
I am really stranded and don't know to do this. I have been trying to look at similar examples but can't seem to find this out. How many valid pavement can I make with the requirement met?