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Year 2022, Volume: 10 Issue: 1, 118 - 126, 15.04.2022

Can Murat Dikmen Mustafa Altınsoy

Abstract

References

  • [1] Horadam, A. F. “Jacobsthal Representation Numbers.” Fib. Quart. 34, 40-54, 1996.
  • [2] Sobczyk, G.. The Hyperbolic Number Plane, The College Mathematics Journal, 26(4), (1995) 268–280.
  • [3] A. E. Motter and A. F. Rosa, Hyperbolic calculus, Adv. Appl. Clifford Algebr., 8(1), (1998), 109-128.
  • [4] F. Torunbalcı Aydın, On generalisations of the Jacobsthal Sequence, Notes on Number Theory and Discrete Mathematics, Online ISSN
  • [5] F. Torunbalcı Aydın, Hyperbolic Fibonacci Sequence, Universal Journal of Mathematics and Applications, Cilt 2, Sayı 2, (2019), 59-62.
  • [6] Y.Soykan, On Dual Hyperbolic Generalized Fibonacci Numbers. Preprints (2019), 2019100172 (doi: 10.20944/preprints201910.0172.v1).
  • [7] Y. Soykan, ve M. G¨ocen, Properties of hyperbolic generalized Pell numbers. Notes on Number Theory and Discrete Mathematics,Vol. 26, (2020), No. 4, 136–153.
  • [8] C. M. Dikmen, Hyperbolic Jacobsthal Numbers, Asian Research Journal of Mathematics, 15 (4) (2019), 1-9. https://doi.org/10.9734/arjom/2019/v15i430153
  • [9] Tas¸yurdu Y. Hyperbolic Tribonacci and Tribonacci-Lucas Sequences, International Journal of Mathematical Analysis Vol. 13, 2019, no. 12, 565 - 572 https://doi.org/10.12988/ijma.2019.91167
  • [10] G. Cerda -Morales, Identities for Third Order Jacobsthal Quaternions, Advances in AppliedCifford Algebras 27(2) (2017), 1043-1053.
  • [11] G. Cerda -Morales, A Note On Dual Third Order Jacobsthal Vectors, Preprints 2017, arXiv:1712.08950v1[math.RA]
  • [12] Charles K. Cook and Michael R. Bacon, Some identities for Jacobsthal and Jacobsthal-Lucas numbers satisfying higher order recurrence relations, Annales Mathematicae et Informaticae, 41 (2013) pp. 27–39.

On Third Order Hyperbolic Jacobsthal Numbers

Year 2022, Volume: 10 Issue: 1, 118 - 126, 15.04.2022

Can Murat Dikmen Mustafa Altınsoy

Abstract

In this paper, we introduce the hyperbolic third order Jacobsthal and Jacobsthal-Lucas numbers and we present recurrence relations, Binet's formulas, generating functions and the summation formulas for these numbers.

Keywords

Third order Jacobsthal numbers third order Jacobsthal-Lucas numbers numbers third order hyperbolic Jacobsthal numbers third order hyperbolic Jacobsthal-Lucas numbers

References

  • [1] Horadam, A. F. “Jacobsthal Representation Numbers.” Fib. Quart. 34, 40-54, 1996.
  • [2] Sobczyk, G.. The Hyperbolic Number Plane, The College Mathematics Journal, 26(4), (1995) 268–280.
  • [3] A. E. Motter and A. F. Rosa, Hyperbolic calculus, Adv. Appl. Clifford Algebr., 8(1), (1998), 109-128.
  • [4] F. Torunbalcı Aydın, On generalisations of the Jacobsthal Sequence, Notes on Number Theory and Discrete Mathematics, Online ISSN
  • [5] F. Torunbalcı Aydın, Hyperbolic Fibonacci Sequence, Universal Journal of Mathematics and Applications, Cilt 2, Sayı 2, (2019), 59-62.
  • [6] Y.Soykan, On Dual Hyperbolic Generalized Fibonacci Numbers. Preprints (2019), 2019100172 (doi: 10.20944/preprints201910.0172.v1).
  • [7] Y. Soykan, ve M. G¨ocen, Properties of hyperbolic generalized Pell numbers. Notes on Number Theory and Discrete Mathematics,Vol. 26, (2020), No. 4, 136–153.
  • [8] C. M. Dikmen, Hyperbolic Jacobsthal Numbers, Asian Research Journal of Mathematics, 15 (4) (2019), 1-9. https://doi.org/10.9734/arjom/2019/v15i430153
  • [9] Tas¸yurdu Y. Hyperbolic Tribonacci and Tribonacci-Lucas Sequences, International Journal of Mathematical Analysis Vol. 13, 2019, no. 12, 565 - 572 https://doi.org/10.12988/ijma.2019.91167
  • [10] G. Cerda -Morales, Identities for Third Order Jacobsthal Quaternions, Advances in AppliedCifford Algebras 27(2) (2017), 1043-1053.
  • [11] G. Cerda -Morales, A Note On Dual Third Order Jacobsthal Vectors, Preprints 2017, arXiv:1712.08950v1[math.RA]
  • [12] Charles K. Cook and Michael R. Bacon, Some identities for Jacobsthal and Jacobsthal-Lucas numbers satisfying higher order recurrence relations, Annales Mathematicae et Informaticae, 41 (2013) pp. 27–39.
There are 12 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Can Murat Dikmen

Mustafa Altınsoy This is me 0000-0001-8384-4636

Publication Date April 15, 2022
Submission Date April 7, 2021
Acceptance Date June 23, 2021
Published in Issue Year 2022 Volume: 10 Issue: 1

Cite

APA Dikmen, C. M., & Altınsoy, M. (2022). On Third Order Hyperbolic Jacobsthal Numbers. Konuralp Journal of Mathematics, 10(1), 118-126.
AMA Dikmen CM, Altınsoy M. On Third Order Hyperbolic Jacobsthal Numbers. Konuralp J. Math. April 2022;10(1):118-126.
Chicago Dikmen, Can Murat, and Mustafa Altınsoy. “On Third Order Hyperbolic Jacobsthal Numbers”. Konuralp Journal of Mathematics 10, no. 1 (April 2022): 118-26.
EndNote Dikmen CM, Altınsoy M (April 1, 2022) On Third Order Hyperbolic Jacobsthal Numbers. Konuralp Journal of Mathematics 10 1 118–126.
IEEE C. M. Dikmen and M. Altınsoy, “On Third Order Hyperbolic Jacobsthal Numbers”, Konuralp J. Math., vol. 10, no. 1, pp. 118–126, 2022.
ISNAD Dikmen, Can Murat - Altınsoy, Mustafa. “On Third Order Hyperbolic Jacobsthal Numbers”. Konuralp Journal of Mathematics 10/1 (April 2022), 118-126.
JAMA Dikmen CM, Altınsoy M. On Third Order Hyperbolic Jacobsthal Numbers. Konuralp J. Math. 2022;10:118–126.
MLA Dikmen, Can Murat and Mustafa Altınsoy. “On Third Order Hyperbolic Jacobsthal Numbers”. Konuralp Journal of Mathematics, vol. 10, no. 1, 2022, pp. 118-26.
Vancouver Dikmen CM, Altınsoy M. On Third Order Hyperbolic Jacobsthal Numbers. Konuralp J. Math. 2022;10(1):118-26.
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