ISL 1979 Problem 35

Given a sequence $(a_n)$ , with $a_1 = 4$ and $a_{n+1} = a_n^2-2 (\forall n \in\mathbb{N})$ , prove that there is a triangle with side lengths $a_{n-1}, a_n, a_{n+1},$ and that its area is equal to an integer.