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 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.

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