I am trying to find a formula for f(x) = a*f(x-1) + b*f(x-2) for x≥1, assuming f(-1) and f(0) are known. In other words, I need some expression for f(x) just in terms of a, b, f(-1), and f(0). I tried plugging in stuff and factoring on paper for the first few iterations, but it quickly got out of control. Then I let Mathematica do the grunt work and tried to see some patterns as x increases. But so far I am only seeing the obvious first couple of terms: a^x * f(0) - (x-1) * a^(x-1) * b * f(0) Any clues? Should I even be doing the problem this way, or is there some simpler method?