Abstract
Gaussian Jacobsthal-Padovan numbers have been the central focus of this paper and firstly this number sequence has defined. Later, we have given the proof of the generating function of the Gaussian Jacobsthal-Padovan sequence. After that by using generating function, we have given the proof of the Binet formula for this number sequence. Additionally, we have investigated some properties such as Simson identity, summation formulas of this sequence. Finally, we have obtained some matrices whose elements are Gaussian Jacobsthal-Padovan numbers.
Keywords
Jacobsthal numbers Jacobsthal-Padovan numbers Gaussian Jacobsthal-Padovan numbers Generating function Binet formula
References
- [1] Koshy T., Fibonacci and Lucas numbers with applications. New York: John Wiley and Sons Inc., (2001).
- [2] Hoggatt V.E. Jr., Fibonacci and Lucas numbers. Boston: Houghton Mifflin Company, (1969).
- [3] Koshy T., Pell and Pell-Lucas numbers with applications. New York: Springer, (2014).
- [4] Horadam A.F., Jacobsthal Representation Numbers, Fibonacci Quarterly, 34 (1) (1996) 40-54.
- [5] Koshy T., Jacobsthal and Jacobsthal-Lucas numbers with applications. New York: John Wiley and Sons Inc., (2001).
- [6] Jordan J.H., Gaussian Fibonacci and Lucas Numbers, Fibonacci Quarterly, 3 (1965) 315-318.
- [7] Halıcı S., Öz S., On Some Gaussian Pell and Pell-Lucas Numbers, Ordu University Journal of Science and Technology, 6 (1) (2016) 8-18.
- [8] Gökbaş H., Köse H., On Complex K-Horadam and Gaussian K-Horadam Sequences, International Journal of Mathematics and Computer Science, 6 (11) (2018) 1938-1942.
- [9] Aşçı M., Gürel E., Gaussian Jacobsthal and Gaussian Jacobsthal-Lucas Numbers, Ars Combinatoria, 111 (2013) 53-63.
- [10] Özkan E., Taştan M., A New Families of Gauss k-Jacobsthal Numbers and Gauss k-Jacobsthal-Lucas Numbers and Their Polynomials, Journal of Science and Arts, 4 (53) (2020) 893-908.
- [11] Cerda-Morales G., On Gauss Third-Order Jacobsthal Numbers and Their Applications, Annals of the Alexandru Ioan Cuza University-Mathematics, 67 (2) (2021) 231-241.
- [12] Sloane N.J.A., The Online Encyclopedia of Integer Sequences. Available at: http://oeis.org/.
- [13] Taşçı D., Gaussian Padovan and Gaussian Pell-Padovan Sequences, Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 67 (2) (2018) 82-88.
- [14] Kartal M.Y., Gaussian Padovan and Gaussian Perrin Numbers and Properties of Them, Asian-Eıropean Journal of Mathematics, 12 (6) (2019) 2040014.
Abstract
References
- [1] Koshy T., Fibonacci and Lucas numbers with applications. New York: John Wiley and Sons Inc., (2001).
- [2] Hoggatt V.E. Jr., Fibonacci and Lucas numbers. Boston: Houghton Mifflin Company, (1969).
- [3] Koshy T., Pell and Pell-Lucas numbers with applications. New York: Springer, (2014).
- [4] Horadam A.F., Jacobsthal Representation Numbers, Fibonacci Quarterly, 34 (1) (1996) 40-54.
- [5] Koshy T., Jacobsthal and Jacobsthal-Lucas numbers with applications. New York: John Wiley and Sons Inc., (2001).
- [6] Jordan J.H., Gaussian Fibonacci and Lucas Numbers, Fibonacci Quarterly, 3 (1965) 315-318.
- [7] Halıcı S., Öz S., On Some Gaussian Pell and Pell-Lucas Numbers, Ordu University Journal of Science and Technology, 6 (1) (2016) 8-18.
- [8] Gökbaş H., Köse H., On Complex K-Horadam and Gaussian K-Horadam Sequences, International Journal of Mathematics and Computer Science, 6 (11) (2018) 1938-1942.
- [9] Aşçı M., Gürel E., Gaussian Jacobsthal and Gaussian Jacobsthal-Lucas Numbers, Ars Combinatoria, 111 (2013) 53-63.
- [10] Özkan E., Taştan M., A New Families of Gauss k-Jacobsthal Numbers and Gauss k-Jacobsthal-Lucas Numbers and Their Polynomials, Journal of Science and Arts, 4 (53) (2020) 893-908.
- [11] Cerda-Morales G., On Gauss Third-Order Jacobsthal Numbers and Their Applications, Annals of the Alexandru Ioan Cuza University-Mathematics, 67 (2) (2021) 231-241.
- [12] Sloane N.J.A., The Online Encyclopedia of Integer Sequences. Available at: http://oeis.org/.
- [13] Taşçı D., Gaussian Padovan and Gaussian Pell-Padovan Sequences, Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 67 (2) (2018) 82-88.
- [14] Kartal M.Y., Gaussian Padovan and Gaussian Perrin Numbers and Properties of Them, Asian-Eıropean Journal of Mathematics, 12 (6) (2019) 2040014.
Details
| Primary Language | English |
|---|---|
| Subjects | Mathematical Sciences |
| Journal Section | Natural Sciences |
| Authors | |
| Publication Date | June 29, 2022 |
| Submission Date | November 18, 2021 |
| Acceptance Date | April 13, 2022 |
| Published in Issue | Year 2022 |