# How to find formula for a series of numbers

Can you tell me how to find logically a formula if series of numbers is given. for example $$2,4,8,16$$ the formula for this series is $2^n$ where $n$ is the $n$-th position. This is an easiest series but lets say a complex series has been given (eg:$0, 12, 10, 0, –12, –20,$) how to find its formula? Advance thanks for your help.

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Conway and Guy "The Book of Numbers" has a section devoted to this topic. –  Mark Bennet Sep 28 '12 at 12:27

$$x^3 − 13 x^2 + 44 x − 32$$