It's easier to treat these as linear difference equations with constant coefficients and use the ansatz of λ^{n}. This is morally the same thing but without the need for matrix manipulation.
Knuth, Oren and Patashnik's Concrete Mathematics is full of these and is required reading for discrete math.
Knuth, Oren and Patashnik's Concrete Mathematics is full of these and is required reading for discrete math.