Some properties of generalized tribonacci quaternions

• Autorzy: Szynal-Liana A. , Włoch I.

Identyfikatory

DOI

10.16926/m.2017.22.06

• Języki publikacji: EN

Abstrakty

EN

In this paper we introduce distinct types of Tribonacci quaternions. We describe dependences between them and we give some their properties also related to a matrix representation.

Słowa kluczowe

EN

quaternions; matrix representation; Tribonacci numbers

PL

kwaternion; macierzowa reprezentacja; numery Tribonacciego

• Wydawca: Wydawnictwo Uniwersytetu Humanistyczno-Przyrodniczego im. Jana Długosza w Częstochowie
• Czasopismo: Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
• Rocznik: 2017
• Tom: Vol. 22
• Strony: 73--81
• Opis fizyczny: Bibliogr. 12 poz., tab.

Twórcy

autor

Szynal-Liana A.

• Rzeszow University of Technology, Faculty of Mathematics and Applied Physics, al. Powstanców Warszawy 12, 35-959 Rzeszów, Poland

autor

Włoch I.

• Rzeszow University of Technology, Faculty of Mathematics and Applied Physics, al. Powstanców Warszawy 12, 35-959 Rzeszów, Poland

Bibliografia

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• [3] M. Feinberg, Fibonacci - Tribonacci, The Fibonacci Quarterly 1.3 (1963), 71-74.
• [4] V. E. Hoggatt Jr, I. D. Ruggles, A primer on the Fibonacci sequence, Part III, The Fibonacci Quarterly 1.3 (1963), 61-65.
• [5] A. F. Horadam, Complex Fibonacci Numbers and Fibonacci Quaternions, American Mathematical Monthly 70 (1963), 289-291.
• [6] A. F. Horadam, Quaternion recurrence relations, Ulam Quarterly 2 (1993), 23-33.
• [7] G. Köhler, Generating functions of Fibonacci-like sequences and decimal expansions of some fractions, The Fibonacci Quarterly 23.1 (1985), 29-35.
• [8] P.-Y. Lin, De Moivre-type identities for the Tribonacci numbers, The Fibonacci Quarterly 26.2 (1988), 131-134.
• [9] W. R. Spickerman, Binet’s formula for the Tribonacci sequence, The Fibonacci Quarterly 20.2 (1982), 118-120.
• [10] A. Szynal-Liana, I. Włoch, A note on Jacobsthal quaternions, Advances in Applied Clifford Algebras 26 (2016), 441-447. doi: https://doi.org/10.1007/s00006-015-0622-1.
• [11] A. Szynal-Liana, I. Włoch, The Pell quaternions and the Pell octonions, Advances in Applied Clifford Algebras 26 (2016), 435-440. doi: https://doi.org/10.1007/s00006-015-0570-9.
• [12] J. P. Ward, Quaternions and Cayley Numbers: Algebra and Applications, Kluwer Academic Publishers, London, 1997.