Matrix Sequences of Tribonacci and Tribonacci-Lucas Numbers

Authors

  • Yüksel Soykan Department of Mathematics, Art and Science Faculty, Zonguldak Bülent Ecevit University, 67100, Zonguldak

DOI:

https://doi.org/10.26713/cma.v11i2.1102

Keywords:

Tribonacci numbers, Tribonacci matrix sequence, Tribonacci-Lucas matrix sequence

Abstract

In this paper, we define Tribonacci and Tribonacci-Lucas matrix sequences and investigate their properties.

Downloads

Download data is not yet available.

References

I. Bruce, A modified Tribonacci sequence, Fibonacci Quarterly 22(3) (1984), 244 – 246. [2] G. Cerda-Morales, On the third-order Jabosthal and third-order Jabosthal-Lucas sequences and their matrix representations, Mediterranean Journal of Mathematics 16 (2019), Article number 32. DOI: 10.1007/s00009-019-1319-9.

E. Choi, Modular tribonacci numbers by matrix method, Journal of Korean Society of Mathematics Education Serries B: Pure and Applied Mathematics 20(3) (2013), 207 – 221, DOI: 10.7468/jksmeb.2013.20.3.207.

H. Civciv and R. Turkmen, On the (s; t)-Fibonacci and Fibonacci matrix sequences, Ars Combinatoria 87 (2008), 161 – 173.

H. Civciv and R. Turkmen, Notes on the (s; t)-Lucas and Lucas matrix sequences, Ars Combinatoria 89 (2008), 271 – 285.

M. Feinberg, Fibonacci-tribonacci, Fibonacci Quarterly 1(3) (1963), 71 – 74.

H. H. Gulec and N. Taskara, On the (s; t)-Pell and (s; t)-Pell-Lucas sequences and their matrix representations, Appl. Math. Lett. 25 (2012), 1554 – 1559, DOI: 10.1016/j.aml.2012.01.014.

F. T. Howard and F. Saidak, Zhou's theory of constructing identities, Congress Numer. 200 (2010), 225 – 237.

L. Marohnic and T. Strmecki, Plastic number: construction and applications, Advanced Research in Scientific Areas (2012), 1523 – 1528.

T. Piezas, A tale of four constants, https://sites.google.com/site/tpiezas/0012.

A. Scott, T. Delaney and V. Hoggatt Jr., Tribonacci sequence, Fibonacci Quarterly 15(3) (1977), 193 – 200, DOI: Missing.

A. Shannon, Tribonacci numbers and Pascal's pyramid, Fibonacci Quarterly 15(3) (1977), 268 – 275, DOI: Missing.

N. J. A. Sloane, The on-line encyclopedia of integer sequences, available at: http://oeis.org.

Y. Soykan, Matrix sequences of Tetranacci and Tetranacci-Lucas numbers, The International Journal of Advances in Applied Mathematics and Mechanics 7(2) (2019), 57 – 69.

W. Spickerman, Binet's formula for the Tribonacci sequence, Fibonacci Quarterly 20 (1981), 118 – 120.

K. Uslu and S. Uygun, On the (s, t) Jacobsthal and (s, t) Jacobsthal-Lucas matrix sequences, Ars Combinatoria 108 (2013), 13 – 22.

S. Uygun and K. Uslu, (s, t)-Generalized Jacobsthal matrix sequences, Springer Proceedings in Mathematics & Statistics, Computational Analysis, Amat, Ankara, (May 2015), 325 – 336, DOI: 10.1007/978-3-319-28443-9_23.

S. Uygun, Some sum formulas of (s, t)-Jacobsthal and (s, t)-Jacobsthal Lucas matrix sequences, Applied Mathematics 7 (2016), 61 – 69, DOI: 10.4236/am.2016.71005.

S. Uygun, The binomial transforms of the generalized (s, t)-Jacobsthal matrix sequence, The International Journal of Advances in Applied Mathematics and Mechanics 6(3) (2019), 14 – 20.

C. C. Yalavigi, Properties of Tribonacci numbers, Fibonacci Quarterly 10(3) (1972), 231 – 246.

Y. Yazlik, N. Taskara, K. Uslu and N. Yilmaz, The generalized (s; t)-sequence and its matrix sequence, Am. Inst. Phys. (AIP) Conf. Proc. 1389 (2012), 381 – 384, DOI: 10.1063/1.3636742.

N. Yilmaz and N. Taskara, Matrix sequences in terms of Padovan and Perrin numbers, Journal of Applied Mathematics 2013 (2013), Article ID 941673, 7 pages, DOI: 10.1155/2013/941673.

N. Yilmaz and N. Taskara, On the negatively subscripted Padovan and Perrin matrix sequences, Communications in Mathematics and Applications, 5(2) (2014), 59 – 72.

A. A. Wani, V. H. Badshah, G. B. S. Rathore and P. Catarino, Generalized Fibonacci and k-Pell matrix sequences, Punjab University Journal of Mathematics 51(1) (2019), 17 – 28.

Downloads

Published

30-06-2020
CITATION

How to Cite

Soykan, Y. (2020). Matrix Sequences of Tribonacci and Tribonacci-Lucas Numbers. Communications in Mathematics and Applications, 11(2), 281–295. https://doi.org/10.26713/cma.v11i2.1102

Issue

Section

Research Article