A Symmetric Algorithm for Hyperharmonic and Fibonacci Numbers
Abstract
In this work, we introduce a symmetric algorithm obtained by the recurrence relation ank=an-1k+ank-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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