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Possible Duplicate:
Summation of series of product of Fibonacci numbers

Find $$\sum_{i=1}^{N-1}F_{i + 1} F_{N + 4 - i}$$

Is there a direct formula to calculate this, rather than actually sum all the terms?

EDIT: My initial summation was incorrect. Updated now.

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    Sasha’s answer to [this very similar question](http://math.stackexchange.com/questions/190443/sum-of-product-of-fibonacci-numbers) may also be useful.2012-09-08
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    Both the questions are a bit different. I also saw a similar question [here](http://stackoverflow.com/questions/12248587/sum-of-products-of-fibonacci-numbers). What I am looking for is a solution like the one in that link (in terms of Lucas or Fibonacci numbers) but for the slightly different summation I have put in the question.2012-09-08
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    Why can't I add comments to other posts?2012-09-08
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    The questions are *substantially* similar. Just take the answer to one, subtract one term, and you have the answer to this one. Please provide some motivation for why you need such a trivial variation?2012-09-08
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    You need a higher reputation in order to add comments to posts that you aren't attached to.2012-09-08
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    Oops...my initial question was incorrect. I have updated it now.2012-09-08
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    I've changed your answer that should have been a comment, and it's comments, to comments on this question and Yury's answer.2012-09-09

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