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it is known that given a certain recurrence relation that describes a sequence of numbers, it is often possible to obtain a functionf[n]that directly yields then-th number of the sequence. This is usually accomplished by using powerful techniques involvinggenerating functionsor theZ-transform(see for instance this thread).

My question is: are there equally powerful techniques that allow one to do the reverse, i.e. given the closed-formf[n]of a sequence, obtain one possible recurrence relation that describes the same sequence (even approximately)?

I am mot sure this is the right forum, but at least I see an analogy between Laplace transform and Z-transform and between the above problem and its continuous analog, i.e. given a certain functionf(x), find a differential equation for whichfis a solution.

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# Obtaining recurrence relation from a given sequence

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