Predict next number from a series
I gave wolfram alpha the sequence: $1,3,13,31,57,91,133,183,241$ and it told me a possible closed form would be $4n^2 -10n + 7$ (which turned out to be right for where I was getting the sequence from). What are some ways of doing this given some terms? I have seen recurrences being approached with power series to find generating functions, but don't recall seeing methods for going from some terms into a possible closed form. What are some approaches?