yukicoder No.718 行列のできるフィボナッチ数列道場 (1)

$$\begin{bmatrix} \sum_{i=0}^{N+1} F_i^2 \\F_{N+2}F_{N+1}\\ F_{N+2}^2 \\ F_{N+1}^2 \end{bmatrix}=\begin{bmatrix} 1 & 0 & 1 & 0 \\ 0 & 1 & 1 & 0 \\ 0 & 2 & 1 & 1 \\ 0 & 0 & 1 & 0\end{bmatrix} \begin{bmatrix} \sum_{i=0}^N F_i^2 \\F_{N+1}F_N\\ F_{N+1}^2 \\ F_{N}^2 \end{bmatrix}$$