Let D_k = |1, 2 k, 2 k-1; n, n^2+n+2, n^2; n, n^2+n, n^2+n+2|. If Σ_k=1^n D_k =96, then n is equal to ____.

Let $\displaystyle \mathrm{D}_{\mathrm{k}}=\left|\begin{array}{ccc}1 & 2 k & 2 k-1 \\ n & n^2+n+2 & n^2 \\ n & n^2+n & n^2+n+2\end{array}\right|$. If $\displaystyle \sum_{k=1}^n \mathrm{D}_{\mathrm{k}}=96$, then $\displaystyle n$ is equal to $\displaystyle \_\_\_\_$.