Abstract
In this paper we derive quite general identities for generalized Fibonacci sequences. The results of this paper not only lead to diverse new identities but also include many existing works as special cases.
Similar content being viewed by others
References
Bilgici G.: Two generalizations of Lucas sequence. Appl. Math. Comput. 245, 526–538 (2014)
Campos H., Catarino P., Aires A.P., Vasco P., Borges A.: On some identities of k-Jacobsthal-Lucas numbers. Int. J. Math. Anal. 8, 489–494 (2014)
Falcon S.: On the k-Lucas numbers. Int. J. Contemp. Math. Sci. 6, 1039–1050 (2011)
Falcon S., Plaza A.: The k-Fibonacci sequence and the Pascal 2-triangle. Chaos Soliton. Fract. 33, 38–49 (2007)
Koshy T.: Fibonacci and Lucas numbers with applications. Wiley, New York (2001)
Siar Z., Keskin R.: Some new identities concerning generalized Fibonacci and Lucas numbers. Hacet. J. Math. Stat. 42, 211–222 (2013)
Spivey M.Z.: Fibonacci identities via the determinant sum property. Coll. Math. J. 37, 286–289 (2006)
Yayenie O.: A note on generalized Fibonacci sequences. Appl. Math. Comput. 217, 5603–5611 (2011)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Choo, Y. On the Generalizations of Fibonacci Identities. Results Math 71, 347–356 (2017). https://doi.org/10.1007/s00025-015-0515-6
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00025-015-0515-6