On third-order Jacobsthal numbers and their bihyperbolic generalizations

Gamaliel Morales

Abstract


In this paper, we introduce bihyperbolic third-order Jacobsthal and third-order Jacobsthal--Lucas numbers. In other words, bihyperbolic numbers whose coefficients are consecutive third-order Jacobsthal and third-order Jacobsthal--Lucas numbers. Furthermore, we study one parameter generalizations of bihyperbolic third-order Jacobsthal and third-order Jacobsthal--Lucas numbers and relations between them.

Keywords


Third-order Jacobsthal numbers; third-order Jacobsthal-Lucas numbers; hyperbolic numbers; bihyperbolic numbers; recurrence relation

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References


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DOI: http://dx.doi.org/10.17951/a.2025.79.2.43-56
Date of publication: 2025-12-31 17:50:05
Date of submission: 2025-12-30 21:11:30


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