Some generalized results related to Fibonacci sequence

• Paul, Neeraj Kumar ^[1] ; Saikia, Helen K. ^[1]
  1. [1] Gauhati University

     Gauhati University

     India

     
• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 40, Nº. 3, 2021 (Ejemplar dedicado a: In progress (June 2021). This issue is in progress. Contains articles that are final and fully citable.), págs. 605-617
• Idioma: inglés
• DOI: 10.22199/issn.0717-6279-4269
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• Resumen

  • Cassini's identity states that for the nth Fibonacci number Fn+1Fn-1-Fn2=(-1)n, We generalize Fibonacci sequence in terms of the number of sequences. Fibonacci sequence is the particular case of generating only one sequence. This generalization is used to generalize Cassini’s identity. Moreover we prove few more results which can be seen as  generalized form of the results which hold for Fibonacci sequence.

• Referencias bibliográficas
  • N. K. Paul and H. K. Saikia, “A generalization of Fibonacci sequence”, Proyecciones (Antofagasta, on line), vol. 39, no. 6, pp. 1393-1405,...
  • D. M. Burton, Elementary number theory, 7th ed. Boston, MA: McGraw-Hill, 2011.
  • G. H. Hardy and E. M. Wright, An introduction to the theory of numbers, 6th ed. Oxford: Oxford University Press, 2008.
  • N. J. A. Sloane, “A000045:Fibonacci numbers: F(n) = F(n-1) F(n-2) with F(0) = 0 and F(1) = 1.”, The on-line encyclopedia of integer...