2nd order linear homogeneous recurrences
Question - Find the general solution to the 2nd order homogeneous linear recurrence below, and give a necessary and sufficient condition on x0 and x1 such that the sequence deﬁned by the recurrence is bounded.
2*xn+1 + 3*xn -2*xn-1= 0
I've found the general solution using the auxiliary equation, but I'm not sure how to get a necessary and sufficient condition for it to be bounded. I know that if a sequence converges, it means that it is bounded, but I have no clue what is the requirement for a recurrent sequence to converge. Any help will be greatly appreciated!