engleski

Log-balanced combinatorial sequences

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.

log-balancedness; log-concavity; log-convexity; integer sequences; recurrences; combinatorial inequalities; Motzkin numbers; Schr\

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