A symmetric algorithm for hyperharmonic and Fibonacci numbers

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.