A symmetric algorithm for hyperharmonic and Fibonacci numbers
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摘要
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 applied to hyperharmonic-, ordinary and incomplete Fibonacci and Lucas numbers. An explicit formula for hyperharmonic numbers, general generating functions of the Fibonacci and Lucas numbers are obtained.Besides we define “hyper-Fibonacci numbers”, “hyper-Lucas numbers”. Using these new concepts, some relations between ordinary and incomplete Fibonacci and Lucas numbers are investigated.
论文关键词:Euler–Seidel matrices,Harmonic and hyperharmonic numbers,Ordinary and incomplete Fibonacci and Lucas numbers,Hyper-Fibonacci and hyper-Lucas numbers
论文评审过程:Available online 22 October 2008.
论文官网地址:https://doi.org/10.1016/j.amc.2008.10.013