International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 4, Pages 507-522
Log-balanced combinatorial sequences
1Department of Informatics and Mathematics, Faculty of Agriculture, University of Zagreb, Svetoimunska 25, Zagreb 10000, Croatia
2Department of Marine Sciences, Texas A&M University at Galveston, Galveston TX 77551, Texas, USA
Received 25 July 2004; Revised 9 December 2004
Copyright © 2005 Tomislav Došlić. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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.