A Symmetric Algorithm for Hyperharmonic and Fibonacci Numbers

Details A Symmetric Algorithm for Hyperharmonic and Fibonacci Numbers A Symmetric Algorithm for Hyperharmonic and Fibonacci Numbers

2008-03-31

arxiv.org/abs/0803.4388v1

Mathematics

Number Theory

16 pages

Scientific paper

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.

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