Matrix Sequences of Third-Order Pell and Third-Order Pell -Lucas Numbers
Keywords:
third-order Pell numbers, third-order Pell matrix sequence, third-order Pell-Lucas matrix sequence.
Abstract
In this paper, we define third-order Pell and third-order Pell-Lucas matrix sequences and investigate their properties.
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References
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Soykan, Y., Matrix Sequences of Tetranacci and Tetranacci-Lucas Numbers, Int. J. Adv. Appl. Math. and Mech. 7(2), 57-69, 2019.
Soykan, Y., On Generalized Third-Order Pell Numbers, Asian Journal of Advanced Research and Reports, 6(1): 1-18, 2019.
Soykan, Y., Matrix Sequences of Tribonacci and Tribonacci-Lucas Numbers, accepted, Communication in Mathematics and Applications, accepted.
Y. Soykan, Tribonacci and Tribonacci-Lucas Matrix Sequences with Negative Subscripts, Communication in Mathematics and Applications, accepted.
K. Uslu, and Ş. Uygun, On the (s,t) Jacobsthal and (s,t) Jacobsthal-Lucas Matrix Sequences, Ars Combin. 108 (2013), 13-22.
Ş. Uygun, and K. Uslu, (s,t)-Generalized Jacobsthal Matrix Sequences, Springer Proceedings in Mathematics&Statistics, Computational Analysis, Amat, Ankara, (May 2015), 325-336.
Ş. Uygun, 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.
S. Uygun, The binomial transforms of the generalized (s,t)-Jacobsthal matrix sequence, Int. J. Adv. Appl. Math. and Mech. 6(3) (2019), 14--20.
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, https://doi.org/10.1063/1.3636742.
N. Yilmaz and N. Taskara, 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.
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 and G. B. S. Rathore, Generalized Fibonacci and k-Pell Matrix Sequences, Punjab University Journal of Mathematics, 50(1) (2018), 68-79.
H. Civciv, and R. Turkmen, On the (s; t)-Fibonacci and Fibonacci matrix sequences, Ars Combin. 87 (2008) 161-173.
H. Civciv and R. Turkmen, Notes on the (s; t)-Lucas and Lucas matrix sequences, Ars Combin. 89 (2008) 271-285.
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.org/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.
N. J. A. Sloane, The on-line encyclopedia of integer sequences, http://oeis.org/
Soykan, Y., Matrix Sequences of Tetranacci and Tetranacci-Lucas Numbers, Int. J. Adv. Appl. Math. and Mech. 7(2), 57-69, 2019.
Soykan, Y., On Generalized Third-Order Pell Numbers, Asian Journal of Advanced Research and Reports, 6(1): 1-18, 2019.
Soykan, Y., Matrix Sequences of Tribonacci and Tribonacci-Lucas Numbers, accepted, Communication in Mathematics and Applications, accepted.
Y. Soykan, Tribonacci and Tribonacci-Lucas Matrix Sequences with Negative Subscripts, Communication in Mathematics and Applications, accepted.
K. Uslu, and Ş. Uygun, On the (s,t) Jacobsthal and (s,t) Jacobsthal-Lucas Matrix Sequences, Ars Combin. 108 (2013), 13-22.
Ş. Uygun, and K. Uslu, (s,t)-Generalized Jacobsthal Matrix Sequences, Springer Proceedings in Mathematics&Statistics, Computational Analysis, Amat, Ankara, (May 2015), 325-336.
Ş. Uygun, 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.
S. Uygun, The binomial transforms of the generalized (s,t)-Jacobsthal matrix sequence, Int. J. Adv. Appl. Math. and Mech. 6(3) (2019), 14--20.
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, https://doi.org/10.1063/1.3636742.
N. Yilmaz and N. Taskara, 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.
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 and G. B. S. Rathore, Generalized Fibonacci and k-Pell Matrix Sequences, Punjab University Journal of Mathematics, 50(1) (2018), 68-79.
Published
2020-03-12
How to Cite
Soykan, Y. (2020). Matrix Sequences of Third-Order Pell and Third-Order Pell -Lucas Numbers. Journal of Progressive Research in Mathematics, 16(1), 2861-2876. Retrieved from http://scitecresearch.com/journals/index.php/jprm/article/view/1842
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