title: Sum of products of Fibonacci numbers
body: <p>Given a series </p>
  
  <p>Fib(1) * Fib (n+2) + Fib(2) * Fib(n+1) + Fib(3) * Fib(n) + ......  + Fib(n-1) * Fib(4) </p>
  
  <p>or Summation  <strong>Fib(x) * Fib (n-x+3)</strong> where x varies from 1 to n-1
  where Fib(n) is nth number of Fibonacci series</p>
  
  <p>to evaluate this series Fib(n) can be calculated using matrix exponentiation . </p>
  
  <p>But the complexity for this is logn and for the n terms it would be nlogn .</p>
  
  <p><strong>I want this series to get reduced to a single term or some other optimization to improve</strong> *<em>the time complexity .</em>*</p>
  
  <p>Any suggestions ??</p>