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.
Categories: math.NT math.CO