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<p>We introduce a new family of hypercomplex numbers by using third-order <i>k</i>-Jacobsthal numbers. These sequences are called the third-order <i>k</i>-Jacobsthal 2<sup><i>r</i></sup>-ions. We present some algebraic properties of the third order <i>k</i>-Jacobsthal 2<sup><i>r</i></sup>-ions, such as the recurrence relation, the Binet formula, generating function, exponential generation function, the d’Ocagne identity, and the Cassini identity. Further, we obtain the matrix representation of the third-order <i>k</i>-Jacobsthal 2<sup><i>r</i></sup>-ions.</p>

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On Hypercomplex Numbers with Third-Order K-jacobsthal Numbers

  • 期刊论文

  • 发表日期：

    2025年12月12日

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  • Gamaliel Morales

摘要

We introduce a new family of hypercomplex numbers by using third-order k-Jacobsthal numbers. These sequences are called the third-order k-Jacobsthal 2r-ions. We present some algebraic properties of the third order k-Jacobsthal 2r-ions, such as the recurrence relation, the Binet formula, generating function, exponential generation function, the d’Ocagne identity, and the Cassini identity. Further, we obtain the matrix representation of the third-order k-Jacobsthal 2r-ions.