You simply must add some tools to your bag of tricks. When faced with a bunch of data, it's just no good to have no idea how to proceed.
1) Did you graph the data?
2) If so, what did it look like? Polynomial? Exponential?
3) Do you know how to look for these relationships?
4) Have you ever heard of a "Difference"? In this case, the "Third Difference" is VERY revealing, but you'll neve know that if you don't know what it is.
Let's see what you get.