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What is the generating function G(z) for the sequence of Fibonacci numbers?
asked in Algorithms by (311 points)   | 164 views

2 Answers

+3 votes

Fibonacci series :  1,1,2,3,5,8,13..........

Its generating function is :

1*z+ 1*z+2*z+3*z+5*z4+-----------∞  =  G(z)

Above series can be rewritten as :

1 + (z +z2) + (z+z2)+....................∞  = G(z)

1/(1 - (z+z2)   = G(z)

Hence generating function G(z) =  1/(1- z -z2)

 

 

answered by Loyal (3.4k points)  
will you please explain in brief
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