$\newcommand{\Fib}{\operatorname{Fib}}$I am trying to reduce this expression for the $n$th term of sequence $G$.
$G[n]=\Fib(4) \times \Fib(n-1) + \Fib(5) \times \Fib(n-2) + \Fib(6) \times \Fib(n-3)+ \cdots +\Fib(n+3) \times \Fib(1)$
Here $\Fib()$ is the Fibonacci sequence $1,2,3,5,8,13, \ldots$
How can I simplify expression for $G[n]$?
I have read the various identities given on Wikipedia but have not been able to apply them. Any help will be highly appreciated, as I have been stuck on this for two days.