Here is my problem and my attempt at the answer. Any help or advice is highly appreciated.(adsbygoogle = window.adsbygoogle || []).push({});

Problem

With the famous sequence of Lucas numbers 1, 3, 4, 7, 11, 18... (Where each number is the sum of the last two and the first two are defined as 1 and 3.) use generating functions to find an explicit formula for the Lucas function.

Attempted Solution

We have

[tex]\sum_{j=1}^{n}F_jx^j[/tex]

where F_{j}denotes the j^{th}Fibonacci number and n is going to infinity. Then we add that to

[tex]\sum_{j=-1}^{n}F_jx^j^+^2[/tex]

Where F_{-1}= -1 and F_{0}= 0

And that should get us a function of Lucas numbers right?

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# Lucas Numbers and Generating Functions

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