I've been struggling in my Discrete math class and the midterm

If you need to study for an exam, 4chan isn't enough. Talk to your TAs, ask the department head, or consult with your university student programs. Chances are your syllabus for the course even lists the university's student help program contact info.

You need a long term solution to your problem, not help with one question.

>>279021

The short version is that any case can be described as a combination of (a)s and (b)s. This combination wouldn't be unique for that W(n) case; there would be different placements and set selections that fit.

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14KB, 473x427px

I've found a solution but I have no idea where they got:
When n >2, W(n) = 2W(n-1) + 3W(n-2)
The rest is simple but Im just not understanding where the equation came from

>>279033

W(n) is the number of ways to tile the board of size n.
2W(n-1) represents placing a red or blue 1x1 piece on the edge of the board. This leaves a 1x(n-1) sized board to cover, which can be covered in W(n-1) ways.
3W(n-2) represents placing a black, green, or white 1x2 piece on the edge of the board. This leaves a 1x(n-2) sized board to cover.

The total number of ways to cover the board is therefore
W(n) = 2W(n-1) + 3W(n-2)