Centaurs on a chess board (noch nicht übersetzt)

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 8x8 board.

It can be shown that at most n² non-attacking centaurs can be placed on a board of size 2n×2n.
Let C(n) be the number of ways to place n² centaurs on a 2n×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 F₁ = F₂ = 1 and F_i = F_i-1 + F_i-2 for i > 2.

Find $\displaystyle \left( \sum_{i=2}^{90} C(F_i) \right) \text{mod } (10^8+7)$.