Discrete Math

What patterns do you notice in what kinds of recursive definitions give rise to what kinds of closed-form solutions? Think about when you see polynomial functions come up in closed-form solutions, when you see exponential functions come up in closed-form solutions, etc. Give some examples of recurrence relations where you'd have a reasonably good guess about what kind of closed-form solutions you'd expect to see, and some examples where you wouldn't know what kind of closed-form solution to expect.

BONUS: if you have any experience with differential equations, you might see some connections! If this is something you've seen, talk about any connections you notice!