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Padovan and Lucas­Padovan Quaternions

박기섭|이광연
한국수학교육학회|2024.11|이론수학과 교직수학 (Theoretical Mathematics and Pedagogical Mathematics)|제31권 제4호|pp. 427-437|DOI 10.7468/jksmeb.2024.31.4.427

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키워드

Padovan numberquaternionsLucas-Padovan number
주제분류수학

초록

In this paper, we introduce the Lucas-Padovan quaternions sequence. Initiating the studies based on the Padovan quaternion coe cients in relation to their recurrence, their matrix representation is then de ned. We investigate various aspects of these quaternions, including summation formulas and binomial sums.

Abstract

In this paper, we introduce the Lucas-Padovan quaternions sequence. Initiating the studies based on the Padovan quaternion coe cients in relation to their recurrence, their matrix representation is then de ned. We investigate various aspects of these quaternions, including summation formulas and binomial sums.

참고문헌 (13)

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  2. H. Gunay, "Some properties of Padovan quaternions", Asian-European Journal of Mathematics, 12, pp.8~ (2019)[DOI]
  3. S. Halici, "On complex Fibonacci quaternions", Adv. Appl. Clifford Algebras, 23, pp.105~112 (2013)[DOI]
  4. S. Halici, "On Fibonacci quaternions matrix", Notes on Number Theory and Discrete Mathematics, 27, pp.236~244 (2021)[DOI]
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  6. K. Lan, "Linear quaternion differential equations: basic theory and funda-mental results", Studies in Applied Mathematics, 141, pp.3~45 (2018)[DOI]
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  8. S. Stevic, "Representation of solitions if bilinear difference quations in terms of gen-eralized fibonacci sequences", Electron. J. Qual. Theory Differ. Equ, 67, pp.1~15 (2014)[DOI]
  9. A. Szynal-Liana, "The Pell quaternions and the Pell Octonions", Adv. Appl. Clifford Algebras, 26, pp.435~440 (2016)[DOI]
  10. A. Szynal-Liana, "A note on Jacobsthal quaterninos", Adv. Appl. Clifford Algebras, 26, pp.441~447 (2016)[DOI]
  11. D. Tasci, "Padovan and Pell-Padovan quaternions", Journal of Science and Arts, 42, pp.125~132 (2018)
  12. ÄU. Toke»ser, "On Pell and Pell-Lucas generalized oc-tonions", Turkish Journal of Mathematics and Computer Science, 13, pp.226~233 (2021)[DOI]
  13. S. YÄuce, "Generalized Dual Fibnacci quaternions", Applied Mathematics E-notes, 16, pp.276~289 (2016)

관련 논문AI추천

Generalized Padovan sequencesJhon J. Bravo, Jose L. Herrera대한수학회 · 대한수학회논문집2022 · 제37권 제4호SOME FAMILIES OF IDENTITIES FOR PADOVAN NUMBERSTARAS GOY장전수학회 · Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집)2018 · 제21권 제3호Roots of Some Equations with Generalized Fibonacci Quaternionic CoefficientsGonca Kizilaslan, Ilker Akkus, Rogério Serôdio경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2025 · 제63권 제3호The Exponential Representations of Pell and Its Generalized Matrix SequencesSukran Uygun경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2024 · 제64권 제3호Some properties of the generalized Fibonacci sequence $\{q_n\}$ by matrix methods전상표, 최광호강원경기수학회 · 한국수학논문집2016 · 제24권 제4호Some Properties of (p, q) - Lucas NumberAlongkot Suvarnamani경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2016 · 제56권 제2호

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