On Non-Newtonian Horadam Numbers

Hasan Gökbaş

doi:10.47000/tjmcs.1606669

On Non-Newtonian Horadam Numbers

Abstract

In this paper, we give some properties of the non-Newtonian Horadam numbers, among others the Binet formula, generating function formula and the general bilinear index-reduction formula which implies d'Ocagne, Vajda, Halton, Catalan, Cassini, Ruggles and Honsberger identities. We also give the matrix representation and some sum formulas of the non-Newtonian Horadam numbers.

Keywords

References

Adegoke, K., Frontczak, R., Goy, T., Reciprocal series involving Horadam numbers, Ukrainian Mathematical Journal, 75(3)(2023), 335–346.
Bashirov, A.E., Relativistic Velocity Addition and Calculi Based on Hyperbolic Tangent. In: Focus on Calculus, Nova Science Publisher, New York, 2020.
Boruah, K., Hazarika, B., Some basic properties of bigeometric calculus and its applications in numerical analysis, Afrika Matematika, 32(2021), 211–227.
Brod, D., On some properties of split Horadam quaternions, Acta Univ. Sapientiae Mathematica, 12(2)(2020), 260–271.
Çakmak, A.F., Başar, F., On the classical sequence spaces and non-Newtonian calculus, J. Inequal. Appl., 12(2012), 932734.
Daşdemir, A., On Horadam-Lucas sequence, Journal of the Indonesian Mathematical Society, 29(1)(2023), 116–124.
Değirmen, N., Duyar, C., A new perspective on Fibonacci and Lucas numbers, Filomat, 37(28)(2023), 9561–9574.
Grossman, M., Katz, R., Non-Newtonian calculus, Lee Press, Pigeon Cove, Massachusetts, 1972.

Details

Primary Language

English

Subjects

Algebra and Number Theory

Journal Section

Research Article

Authors

Hasan Gökbaş ^*
0000-0002-3323-8205
Türkiye

Publication Date

June 30, 2026

Submission Date

December 24, 2024

Acceptance Date

December 19, 2025

Published in Issue

Year 2026 Volume: 18 Number: 2

DOI

https://doi.org/10.47000/tjmcs.1606669

IZ

https://izlik.org/JA46FS53KG

Cite

RIS / Bibtex

APA

Gökbaş, H. (2026). On Non-Newtonian Horadam Numbers. Turkish Journal of Mathematics and Computer Science, 18(2), 303-309. https://doi.org/10.47000/tjmcs.1606669

AMA

1.Gökbaş H. On Non-Newtonian Horadam Numbers. TJMCS. 2026;18(2):303-309. doi:10.47000/tjmcs.1606669

Chicago

Gökbaş, Hasan. 2026. “On Non-Newtonian Horadam Numbers”. Turkish Journal of Mathematics and Computer Science 18 (2): 303-9. https://doi.org/10.47000/tjmcs.1606669.

EndNote

Gökbaş H (June 1, 2026) On Non-Newtonian Horadam Numbers. Turkish Journal of Mathematics and Computer Science 18 2 303–309.

IEEE

[1]H. Gökbaş, “On Non-Newtonian Horadam Numbers”, TJMCS, vol. 18, no. 2, pp. 303–309, June 2026, doi: 10.47000/tjmcs.1606669.

ISNAD

Gökbaş, Hasan. “On Non-Newtonian Horadam Numbers”. Turkish Journal of Mathematics and Computer Science 18/2 (June 1, 2026): 303-309. https://doi.org/10.47000/tjmcs.1606669.

JAMA

1.Gökbaş H. On Non-Newtonian Horadam Numbers. TJMCS. 2026;18:303–309.

MLA

Gökbaş, Hasan. “On Non-Newtonian Horadam Numbers”. Turkish Journal of Mathematics and Computer Science, vol. 18, no. 2, June 2026, pp. 303-9, doi:10.47000/tjmcs.1606669.

Vancouver

1.Hasan Gökbaş. On Non-Newtonian Horadam Numbers. TJMCS. 2026 Jun. 1;18(2):303-9. doi:10.47000/tjmcs.1606669