APPLIED MATHEMATICS AND COMPUTATION, vol.206, no.2, pp.942-951, 2008 (SCI-Expanded)
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 de. ne "hyper-Fibonacci numbers", "hyper-Lucas numbers". Using these new concepts, some relations between ordinary and incomplete Fibonacci and Lucas numbers are investigated. (c) 2008 Elsevier B. V. All rights reserved.