Some generalized results related to Fibonacci sequence




Fibonacci sequence, Cassini’s identity


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.

Author Biographies

Neeraj Kumar Paul, Gauhati University.

Dept. of Mathematics.

Helen K. Saikia, Gauhati University,

Dept. of Mathematics


N. K. Paul and H. K. Saikia, “A generalization of Fibonacci sequence”, Proyecciones (Antofagasta, on line), vol. 39, no. 6, pp. 1393-1405, 2020, doi: 10.22199/issn.0717-6279-2020-06-0085

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 sequences. The OEIS Foundation , 2011 [Online]. Available:



How to Cite

N. K. Paul and H. K. Saikia, “Some generalized results related to Fibonacci sequence”, Proyecciones (Antofagasta, On line), vol. 40, no. 3, pp. 605-617, Apr. 2021.