  We consider log-convex sequences that satisfy an additional constraint
imposed on their rate of growth. We call such sequences log-balanced. It is
shown that all such sequences satisfy a pair of double inequalities. Sufficient
conditions for log-balancedness are given for the case when the sequence
satisfies a two- (or more-) term linear recurrence. It is shown that many
combinatorially interesting sequences belong to this class, and, as a
consequence, that the above-mentioned double inequalities are valid for all of
them.
