I am wondering if there's some tip for guessing the degree of a function or if it really is just a guess (assuming one doesn't know all the inner workings of what produced the number in the first place).
I ask because if I guess the degree and get the recurrence coefficients, sometimes if I undershoot the degree, the coefficients are integers but they turn out to be wrong.
Is it really just guess and check? Guess the degree, get the coefficients, test it against the sequence, if it doesn't work, increase the degree and try again, etc?