Let \(\displaystyle A = \begin{bmatrix} 1 & a & a \\ 0 & 1 & b \\ 0 & 0 & 1 \end{bmatrix}\), \(\; a, b \in \mathbb{R}. \) If for some \(\displaystyle n \in N, A^n = \begin{bmatrix} 1 & 48 & 2160 \\ 0 & 1 & 96 \\ 0 & 0 & 1 \end{bmatrix}\) then \( n + a + b \) is equal to \( \_ \_ \_ \_ \_ \_ \).
