Probably the simplest thing to do would be to calculate what multiplying M by an arbitrary 2 x 2 matrix would give:

Now you can set up a recursion: for a = 5, b = 2, c = -1, and d = 2. This generates the next set of a, b, c, and d.

So , , etc.

Now solve the system of recursions. (That step is beyond me, I'm afraid!)

-Dan