  The partition function $p(n)$ and many of its related restricted partition
functions have recently been shown independently to satisfy log-concavity:
$p(n)^2 \geq p(n-1)p(n+1)$, and satisfy the inequality: $p(n)p(m) \geq p(n+m)$
with only finitely many instances of equality or failure. This paper proves
that this is no coincidence, that any log-concave sequence $\{x_n\}$ satisfying
a particular initial condition likewise satisfies the inequality $x_nx_m \geq
x_{n+m}$. This paper further determines that these conditions are sufficient
but not necessary and considers various examples to illuminate the situation.
