What are some algorithms for finding a closed form function given an integer sequence?

Question

I\'m looking form a programatic way to take an integer sequence and spit out a closed form function. Something like:

Given: 1,3,6,10,15

Return: n(n+1)/2

Answer 1

I think your problem is ill-posed. Given any finite number of integers in a sequence with no generating function, the next element can be anything.

You need to assume something about the sequence. Is it geometric? Arithmetic?