What is the best way to find generating function of a given sequences ?

In many problems we need to find the generating function of given sequence like Fibonacci,Tribinocci,Lucas numbers. My question is what is the best way by which we get the generating function of a sequence , and suggest me if there are there any tools regarding these to analyses of these sequences ?

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This can be one best solution as far as I know …!!

Please suggest me anything other then this.

Thanks in advance.!

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The generating function, as far as I know it is only useful to derive the characteristic equation that will allow one to obtain a “closed-form” expression to compute the N-th fibonnaci number directly…

On the case of the Fibonacci series, the generating function is a power series, of the form:

F(k)*x^k summed for k = 0 to +infinity, where F(k9 is the k-th Fibonacci number… The series is convergent if abs(x) < (1/phi) where phi is the golden ratio…

All is explained relatively well on wikipedia :smiley:

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