Advances in Difference Equations 
Volume 2004 (2004), Issue 4, Pages 273-277
doi:10.1155/S1687183904310034

On the growth rate of generalized Fibonacci numbers

Donniell E. Fishkind

 Department of Applied Mathematics and Statistics, The Johns Hopkins University, Baltimore 21218-2682, MD, UK
Received 1 May 2004

Abstract

Let α(t) be the limiting ratio of the generalized Fibonacci numbers produced by summing along lines of slope t through the natural arrayal of Pascal's triangle. We prove that α(t)3+t is an even function.