  In this paper, we give an explicit expression for a certain family of ternary
cyclotomic polynomials: specifically $\Phi_{p_{1}p_{2}p_{3}}$, where
$p_{1}<p_{2}<p_{3}$ are odd primes such that $p_{2} \equiv1 \mod p_{1}$ and
$p_{3} \equiv1 \mod {p_{1}p_{2}}$. As an application of the explicit
expressions, we give an exact formula for the number of nonzero terms in the
polynomials in the family, which in turn immediately shows that the density
(number of non-zeros terms / degree) is roughly inversely proportional to
$p_{2}$, when $p_{1}$ is sufficiently large.
