EN
On Gaussian Jacobsthal-Padovan Numbers
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
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.
Details
Primary Language
English
Subjects
Mathematical Sciences
Journal Section
Research Article
Authors
Publication Date
June 29, 2022
Submission Date
November 18, 2021
Acceptance Date
April 13, 2022
Published in Issue
Year 2022 Volume: 43 Number: 2