Question 60
For a sequence $a_{1} \lt a_{2} \lt \cdots \lt a_{n}$ of integers, a pair $(a_{i}, a_{j})$ with $1 \leq i \lt j \leq n$ is called interesting if there exists a pair $(a_{k}, a_{l})$ of integers with $1 \leq k \lt l \leq n$ such that
$$
\frac{a_{l} - a_{k}}{a_{j} - a_{i}} = 2
$$
For each $n \geq 3$, find the largest possible number of interesting pairs in a sequence of length $n$.
$$
\frac{a_{l} - a_{k}}{a_{j} - a_{i}} = 2
$$
For each $n \geq 3$, find the largest possible number of interesting pairs in a sequence of length $n$.