Sums of generalized third-order Jacobsthal numbers by matrix methods

Authors

DOI:

https://doi.org/10.5540/tcam.2025.026.e01817

Keywords:

Recurrence, sum, matrix method, companion matrix, third-order Jacobsthal number.

Abstract

In this paper, we consider a certain third-order linear recurrence and then give generating matrices for the sums of positively and negatively subscripted terms of this recurrence. Further, we use matrix methods and derive explicit formulas for these sums.

References

Cerda-Morales, G. Identities for third order Jacobsthal quaternions. Advances in Applied Clifford Algebras 2017; 27 (2): 1043-1053.

Cerda-Morales, G. Dual third-order Jacobsthal quaternions. Proyecciones Journal of Mathematics 2018; 37(4): 731-747.

Cook, C. K., Bacon, M. R. Some identities for Jacobsthal and Jacobsthal-Lucas numbers satisfying higher order recurrence relations. Annales Mathematicae et Informaticae 2013; 41: 27-39.

Er, M. C. Sums of Fibonacci numbers by matrix methods. The Fibonacci Quarterly 1984; 22(3): 204-207.

Horadam, A. F. Jacobsthal representation numbers. The Fibonacci Quarterly 1996; 43(1): 40-54.

Kilic, E. Tribonacci sequences with certain indices and theri sums. Ars Combinatoria 2008; 86: 13-22.

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Published

2025-09-03

How to Cite

Cerda-Morales, G. (2025). Sums of generalized third-order Jacobsthal numbers by matrix methods. Trends in Computational and Applied Mathematics, 26(1), e01817. https://doi.org/10.5540/tcam.2025.026.e01817

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Section

Original Article