Alographite for the analysis of a series

Question

Is there an algorithm that can find a recursive relation that causes a given series?

For instance:

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

Enter this series in the algorithm, and it will recognize the “most mean” (or one of the most mean) repetition relationships. In my example, the equation

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

Answer 1

Definitely not. In the general case, this problem rises to the Kolmogorov complexity problem, which is incomputable in terms of the theory of algorithms.

Maybe if you add conditions for your function (for example, it is a polynomial with discrete coefficients and powers) - then you will have a chance.