International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 4, Pages 507-522
doi:10.1155/IJMMS.2005.507
Log-balanced combinatorial sequences
Tomislav Došlić
Department of Informatics and Mathematics, Faculty of Agriculture, University of Zagreb, Sveto {s}imunska 25, Zagreb 10000, Croatia
Abstract
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.