Alogrithm to analyze series [closed]

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Is there an algorithm that can find the recurrence relation causing a given serie?

For example:

Serie: 1, 3, 7, 15, 31, 63, 127

Enter this serie in an algorithm and it finds out the "most parsimonious" (or one of the most parsimonious) recurrence relation. In my example, the equation is

x(t+1) = x(t)*2 + 1

Answer 1

Definitely not. In common case this problem upcomes to Kolmogorov complexity problem, which is incomputable in terms of algorithm theory.

May be, if you'll add conditions for your function (for example, it is polynom with discrete coefficients and powers) - then you'll have a chance.