On a chess board, a centaur moves like a king or a knight. The diagram below shows the valid moves of a centaur (represented by an inverted king) on an $8\times 8$ board.

It can be shown that at most $n^2$ non-attacking centaurs can be placed on a board of size $2n\times 2n$.
Let $C(n)$ be the number of ways to place $n^2$ centaurs on a $2n\times 2n$ board so that no centaur attacks another directly.
For example $C(1)=4$, $C(2)=25$, $C(10)=1477721$.

Let $F_i$ be the $i$^th Fibonacci number defined as $F_1=F_2=1$ and $F_i=F_{i-1}+F_{i-2}$ for $i>2$.

Find ${\displaystyle (\sum _{i=2}^{90}C(F_i))mod({10}^8+7)}$.