A symmetric algorithm for hyperharmonic and Fibonacci numbers

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DİL A., Mezö I.

APPLIED MATHEMATICS AND COMPUTATION, cilt.206, sa.2, ss.942-951, 2008 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 206 Sayı: 2
  • Basım Tarihi: 2008
  • Doi Numarası: 10.1016/j.amc.2008.10.013
  • Dergi Adı: APPLIED MATHEMATICS AND COMPUTATION
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.942-951
  • Anahtar Kelimeler: Euler-Seidel matrices, Harmonic and hyperharmonic numbers, Ordinary and incomplete Fibonacci and Lucas numbers, Hyper-Fibonacci and hyper-Lucas numbers
  • Akdeniz Üniversitesi Adresli: Evet

Özet

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.