On Matrix Sequence of modified Tribonacci-Lucas Numbers

Year 2022, , 217 - 227, 31.12.2022

Yüksel Soykan , Erkan Taşdemir , Vedat İrge

https://doi.org/10.51354/mjen.894514

Cited By: 1

Abstract

In this paper, we define modified Tribonacci-Lucas matrix sequence and investigate its properties.

Keywords

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

References

• [1] Cerda-Morales, G., On the Third-Order Jacobsthal and Third-Order Jacobsthal--Lucas Sequences and Their Matrix Representations. Mediterranean Journal of Mathematics, 16 (2019) 1-12.
• [2] Civciv, H., Turkmen, R., On the (s; t)-Fibonacci and Fibonacci matrix sequences, Ars Combin. 87 (2008) 161-173.
• [3] Civciv, H., Turkmen, R., Notes on the (s; t)-Lucas and Lucas matrix sequences, Ars Combin. 89 (2008) 271-285.
• [4] Gulec, H.H., Taskara, N., On the (s; t)-Pell and (s; t)-Pell-Lucas sequences and their matrix representations, Appl. Math. Lett. 25 (2012), 1554-1559, doi.org/10.1016/j.aml.2012.01.014.
• [5] Soykan, Y., Matrix Sequences of Tetranacci and Tetranacci-Lucas Numbers, Int. J. Adv. Appl. Math. and Mech. 7(2), 57-69, 2019.
• [6] Soykan, Y., Matrix Sequences of Tribonacci and Tribonacci-Lucas Numbers, Communications in Mathematics and Applications, 11(2), 281-295, 2020. DOI: 10.26713/cma.v11i2.1102
• [7] Soykan, Y., Tribonacci and Tribonacci-Lucas Matrix Sequences with Negative Subscripts, Communications in Mathematics and Applications, 11(1), 141159, 2020. DOI: 10.26713/cma.v11i1.1103.
• [8] Soykan, Y., On Four Special Cases of Generalized Tribonacci Sequence: Tribonacci-Perrin, modified Tribonacci, modified Tribonacci-Lucas and adjusted Tribonacci-Lucas Sequences, Journal of Progressive Research in Mathematics, 16(3), 3056-3084, 2020.
• [9] Uslu, K., Uygun, Ş., On the (s,t) Jacobsthal and (s,t) Jacobsthal-Lucas Matrix Sequences, Ars Combin. 108 (2013), 13-22.
• [10] Uygun, Ş., Uslu, K., (s,t)-Generalized Jacobsthal Matrix Sequences, Springer Proceedings in Mathematics&Statistics, Computational Analysis, Amat, Ankara, (May 2015), 325-336.
• [11] Uygun, Ş., Some Sum Formulas of (s,t)-Jacobsthal and (s,t)-Jacobsthal Lucas Matrix Sequences, Applied Mathematics, 7 (2016), 61-69, http://dx.doi.org/10.4236/am.2016.71005.
• [12] Uygun, Ş., The binomial transforms of the generalized (s,t)-Jacobsthal matrix sequence, Int. J. Adv. Appl. Math. and Mech. 6(3) (2019), 14-20.
• [13] Yazlik, Y., Taskara, N., Uslu K., Yilmaz, N., The generalized (s; t)-sequence and its matrix sequence, Am. Inst. Phys. (AIP) Conf. Proc. 1389 (2012), 381-384, https://doi.org/10.1063/1.3636742.
• [14] Yilmaz, N., Taskara, N., Matrix Sequences in Terms of Padovan and Perrin Numbers, Journal of Applied Mathematics, Volume 2013 (2013), Article ID 941673, 7 pages, http://dx.doi.org/10.1155/2013/941673.
• [15] Yilmaz, N., Taskara, N., On the Negatively Subscripted Padovan and Perrin Matrix Sequences, Communications in Mathematics and Applications, 5(2) (2014), 59-72.
• [16] Wani, A.A., Badshah, V.H., and Rathore, G.B.S., Generalized Fibonacci and k-Pell Matrix Sequences, Punjab University Journal of Mathematics, 50(1) (2018), 68-79.