Abstract
In this paper, we investigate some properties of generalized Fibonacci quaternions and Fibonacci-Narayana quaternions in a generalized quaternion algebra.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
J. P. Allouche, T. Johnson, Nrayana’s Cows and Delayed Morphisms. recherche.ircam.fr/equipes/repmus/jim96/actes/Allouche.ps
I. Cucurezeanu, Exercices in Arithmetics and Numbers Theory. Ed. Tehnică, Bucharest, 1976. [in Romanian]
T. V. Didkivska, M. V. St’opochkina, Properties of Fibonacci-Narayana numbers. In the World of Mathematics 9 (1) (2003), 29–36. [in Ukrainian]
A. Dress, R. Giegerich, S. Grűnewald, H. Wagner, Fibonacci-Cayley Numbers and Repetition Patterns in Genomic DNA. Ann. Comb. 7 (2003), 259–279.
Halici S.: On Fibonacci Quaternions. Adv. in Appl. Clifford Algebras 22((2), 321–327 (2012)
Horadam A.F.: A Generalized Fibonacci Sequence. Amer. Math. Monthly 68, 455–459 (1961)
Horadam A.F.: Complex Fibonacci Numbers and Fibonacci Quaternions. Amer. Math. Monthly 70, 289–291 (1963)
S. Kak, The Golden Mean and the Physics of Aesthetics. Archive of Physics: physics/0411195, 2004, http://arxiv.org/ftp/physics/papers/0411/0411195.pdf.
T. Koshy, Fibonacci and Lucas Numbers with Applications. A Wiley-Interscience publication, U.S.A, 2001.
Singh P.: The So-called Fibonacci Numbers in Ancient and Medieval India. Historia Mathematica 12, 229–244 (1985)
Satyanarayana Murthy P.V.: Fibonacci-Cayley Numbers. The Fibonacci Quarterly 20(1), 59–64 (1982)
A. N. Singh, On the use of series in Hindu mathematics. Osiris 1 1936, p. 606-628. (http://www.anaphoria.com/hindu.PDF)
Singh P.: The so-called Fibonacci numbers in ancient and medieval India. Historia Mathematica 12, 229–244 (1985)
V. Shpakivskyi, On the one property of Fibonacci-Narayana numbers. Mathematics no. 11(359) (2006), 12–14. [in Ukrainian]
Swamy M.N.S.: On generalized Fibonacci Quaternions. The Fibonacci Quaterly 11((5), 547–549 (1973)
A. P. Yushkevich, History of Mathematics in the Middle Ages. Gos. izd. fiz.- mat. lit., Moskow, 1961.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Flaut, C., Shpakivskyi, V. On Generalized Fibonacci Quaternions and Fibonacci-Narayana Quaternions. Adv. Appl. Clifford Algebras 23, 673–688 (2013). https://doi.org/10.1007/s00006-013-0388-2
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00006-013-0388-2