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Some properties of the generalized Fibonacci sequence $\{q_n\}$ by matrix methods

최광호|전상표
강원경기수학회 (The Kangweon-Kyungki Mathematical Society)|2016.12|한국수학논문집 (Korean Journal of Mathematics)|제24권 제4호|pp. 681-691|DOI https://doi.org/10.11568/kjm.2016.24.4.681

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키워드

matrix methodsgeneralized Fibonacci sequencestridiagonal matrices
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초록

In this note, we consider a generalized Fibonacci sequence $\{q_n\}$. We give a generating matrix for $\{q_n\}$. With the aid of this matrix, we derive and re-prove some properties involving terms of this sequence

Abstract

In this note, we consider a generalized Fibonacci sequence $\{q_n\}$. We give a generating matrix for $\{q_n\}$. With the aid of this matrix, we derive and re-prove some properties involving terms of this sequence

참고문헌 (13)

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  3. M. Edson, "The k-periodic Fibonacci sequence and extended Binet's formula", Integer, 11, pp.1~12 (2011)
  4. M. Edson, "A new generalization of Fibonacci sequence and ex-tended Binet's formula", Integer, 9, pp.639~654 (2009)
  5. Y. K. Gupta, "Generalized Fibonacci Sequences", Theoretical Mathematics and Applications, 2(2), pp.115~124 (2012)
  6. Y. K. Gupta, "Generalized Fibonacci-Like Sequence Associated with Fibonacci and Lucas Sequences", Turkish Journal of Analysis and Number Theory, 2(6), pp.233~238 (2014)
  7. A. F. Horadam, "A generalized Fibonacci sequences", Amer. Math. Monthly, 68, pp.455~459 (1961)
  8. E. Kilic, "Sums of the squares of terms of sequence｛un｝", Proc. Indian Acad. Sci.(Math. Sci.), 118(1), pp.27~41 (2008)
  9. D. Kalman, "The Fibonacci numbers - Exposed", The Mathematical Magazine, 2 (2002)
  10. J. R. Silvester, "Fibonacci properties by matrix methods", Mathematical Gazette, 63, pp.188~191 (1979)
  11. K. S. Williams, "The nth power of a 2X2 matrix", Math. Mag, 65(5), pp.336~ (1992)
  12. O. Yayenie, "A note on generalized Fibonacci sequences", Applied Mathematics and Computation, 217, pp.5603~5611 (2011)
  13. H. Zhang, "On the reciprocal sums of the generalized Fibonacci sequences", Adv. Differ. Equ, 2013 (2013)

관련 논문AI추천

Linearlization of generalized Fibonacci sequences장영호, 전상표강원경기수학회 · 한국수학논문집2014 · 제22권 제3호Some Properties of Fibonacci Numbers, Generalized Fibonacci Numbers and Generalized Fibonacci Polynomial SequencesAlexandre Laugier, Manjil P. Saikia경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2017 · 제57권 제1호THE DIFFERENCE MATRICES OF GENERALIZED FIBONACCI AND LUCAS SEQUENCES김익표장전수학회 · Advanced Studies in Contemporary Mathematics2017 · 제27권 제1호The Exponential Representations of Pell and Its Generalized Matrix SequencesSukran Uygun경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2024 · 제64권 제3호Generalized Fibonacci-Feinberg sequencesA.G. Shannon, C. K. Cook장전수학회 · Advanced Studies in Contemporary Mathematics2011 · 제21권 제2호Complex factorizations of the generalized Fibonacci sequences $\{q_n\}$전상표강원경기수학회 · 한국수학논문집2015 · 제23권 제3호

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