행렬 거듭제곱 성분

$\displaystyle A = \begin{pmatrix} 3 & 1 \\ 0 & 1 \end{pmatrix}$, $\displaystyle A ^{2} = \begin{pmatrix} 3 & 1 \\ 0 & 1 \end{pmatrix}$$\displaystyle \begin{pmatrix} 3 & 1 \\ 0 & 1 \end{pmatrix}$$\displaystyle = \begin{pmatrix} 3 ^{2} & 1 + 3 \\ 0 & 1 \end{pmatrix}$, $A ^{3} = AA ^{2}$$\displaystyle = \begin{pmatrix} 3 ^{3} & 1 + 3 + 3 ^{2} \\ 0 & 1 \end{pmatrix}$, … , $\displaystyle A ^{6} = \begin{pmatrix} 3 ^{6} & 1 + 3 + \cdots + 3 ^{5} \\ 0 & 1 \end{pmatrix}$ ∴ $a _{6} = 1 + 3 + \cdots + 3 ^{5} = 364$