2. Given an integer $n \geqslant 2$. Let integers $a_{0}, a_{1}, \cdots, a_{n}$ satisfy $0=a_{0}<a_{1}<\cdots<a_{n}=2 n-1$. Find the minimum possible number of elements in the set $\left\{a_{i}+a_{j} \mid 0 \leqslant i \leqslant j \leqslant n\right\}$.
Let $S=\left\{a_{i}+a_{j} \mid 0 \leqslant i \leqslant j \leqslant n\right\}$.
If $a_{k}=k(k=1,2, \cdots, n-1)$, then
$$
S=\{0,1,2, \cdots, 3 n-2,4 n-2\},
$$

At this point, $|S|=3 n$.
It remains to prove that $|S| \geqslant 3 n$.