A Symmetric Algorithm for Hyperharmonic and Fibonacci Numbers
Number Theory
2008-04-01 v1 Combinatorics
Abstract
In this work, we introduce a symmetric algorithm obtained by the recurrence relation a_{n}^{k}=a_{n-1}^{k}+a_{n}^{k-1}. We point out that this algorithm can be apply to hyperharmonic-, ordinary and incomplete Fibonacci- and Lucas numbers. An explicit formulae for hyperharmonic numbers, general generating functions of the Fibonacci- and Lucas numbers are obtained. Besides we define "hyperfibonacci numbers", "hyperlucas numbers". Using these new concepts, some relations between ordinary and incomplete Fibonacci- and Lucas numbers are investigated.
Cite
@article{arxiv.0803.4388,
title = {A Symmetric Algorithm for Hyperharmonic and Fibonacci Numbers},
author = {Ayhan Dil and Istvan Mezo},
journal= {arXiv preprint arXiv:0803.4388},
year = {2008}
}
Comments
16 pages