Let A= [1, a, a; 0, 1, b; 0, 0, 1], a, b ∈ R. If for some n ∈ N, A^n= [1, 48, 2160; 0, 1, 96; 0, 0, 1] then n+a+b is equal to \ \ \ \.

Let $\displaystyle A=\left[\begin{array}{ccc}1 & a & a \\ 0 & 1 & b \\ 0 & 0 & 1\end{array}\right], a, b \in \mathbb{R}$. If for some $\displaystyle n \in \mathbb{N}, A^n=\left[\begin{array}{ccc}1 & 48 & 2160 \\ 0 & 1 & 96 \\ 0 & 0 & 1\end{array}\right]$ then $\displaystyle n+a+b$ is equal to \_\_\_\_.