A symmetric algorithm for hyperharmonic and Fibonacci numbers


Creative Commons License

DİL A., Mezö I.

APPLIED MATHEMATICS AND COMPUTATION, vol.206, no.2, pp.942-951, 2008 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 206 Issue: 2
  • Publication Date: 2008
  • Doi Number: 10.1016/j.amc.2008.10.013
  • Journal Name: APPLIED MATHEMATICS AND COMPUTATION
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.942-951
  • Keywords: Euler-Seidel matrices, Harmonic and hyperharmonic numbers, Ordinary and incomplete Fibonacci and Lucas numbers, Hyper-Fibonacci and hyper-Lucas numbers
  • Akdeniz University Affiliated: Yes

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 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.