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Year 2021, Volume: 9 Issue: 1, 183 - 189, 28.04.2021

Abstract

References

  • [1] P. Catarino and A. Borges, On Leonardo Numbers, Acta Mathematica Universitatis Comenianae, Vol:89, No.1 (2019), 75–86.
  • [2] P. Catarino and A. Borges, A Note on Incomplete Leonardo Numbers, Integers, Vol:20 (2020).
  • [3] C. Kızılates, On the Quadra Lucas-Jacobsthal Numbers, Karaelmas Science and Engineering Journal, Vol:7, No.2 (2017), 619-621.
  • [4] E. G. Kocer, N. Tuglu and A. Stakhov, On the m extension of the Fibonacci and Lucas p numbers, Chaos, Solitons&Fractals, Vol:40, No.4 (2009), 1890–1906.
  • [5] Koshy, T., Fibonacci and Lucas numbers with Applications, John Wiley&Sons, 2001.
  • [6] A. G. Shannon, A Note On Generalized Leonardo Numbers, Notes on Number Theory and Discrete Mathematics, Vol:25, No. 3 (2019), 97-101.
  • [7] N. J. A. Sloane, The On-line Encyclopedia of Integers Sequences, The OEIS Foundation Inc., http.//oeis.org.
  • [8] R. R. Stone, General identities for Fibonacci and Lucas numbers with polynomial subscripts in several variables, Fibonacci Quarterly, Vol:13 (1975), 289-294.
  • [9] N. Tuglu, C. Kızılates and S. Kesim, On the harmonic and hyperharmonic Fibonacci numbers, Advances Difference Equations, Article number: 297 (2015).
  • [10] Vajda, S., Fibonacci and Lucas numbers and the Golden Section: Theory and Applications, Halsted Press,1989.
  • [11] R. P. M. Vieira, F. R. V. Alves and P. M. Catarino, Relacoes Bidimensiona is E Identidades Da Sequencia De Leonardo, Revista Sergipana de Matematica e Educacao Matematica, No. 2 (2019), 156-173.

Some Properties of Leonardo Numbers

Year 2021, Volume: 9 Issue: 1, 183 - 189, 28.04.2021

Abstract

In this paper, we consider the Leonardo numbers which is defined by Catarino and Borges. Using Binet's formula of this sequence, we obtain new identities of the Leonardo numbers. Also , we give relations among the Fibonacci, Lucas and Leonardo numbers. Finally, using the matrix representation of Leonardo numbers, we obtain some identities of Leonardo numbers.

References

  • [1] P. Catarino and A. Borges, On Leonardo Numbers, Acta Mathematica Universitatis Comenianae, Vol:89, No.1 (2019), 75–86.
  • [2] P. Catarino and A. Borges, A Note on Incomplete Leonardo Numbers, Integers, Vol:20 (2020).
  • [3] C. Kızılates, On the Quadra Lucas-Jacobsthal Numbers, Karaelmas Science and Engineering Journal, Vol:7, No.2 (2017), 619-621.
  • [4] E. G. Kocer, N. Tuglu and A. Stakhov, On the m extension of the Fibonacci and Lucas p numbers, Chaos, Solitons&Fractals, Vol:40, No.4 (2009), 1890–1906.
  • [5] Koshy, T., Fibonacci and Lucas numbers with Applications, John Wiley&Sons, 2001.
  • [6] A. G. Shannon, A Note On Generalized Leonardo Numbers, Notes on Number Theory and Discrete Mathematics, Vol:25, No. 3 (2019), 97-101.
  • [7] N. J. A. Sloane, The On-line Encyclopedia of Integers Sequences, The OEIS Foundation Inc., http.//oeis.org.
  • [8] R. R. Stone, General identities for Fibonacci and Lucas numbers with polynomial subscripts in several variables, Fibonacci Quarterly, Vol:13 (1975), 289-294.
  • [9] N. Tuglu, C. Kızılates and S. Kesim, On the harmonic and hyperharmonic Fibonacci numbers, Advances Difference Equations, Article number: 297 (2015).
  • [10] Vajda, S., Fibonacci and Lucas numbers and the Golden Section: Theory and Applications, Halsted Press,1989.
  • [11] R. P. M. Vieira, F. R. V. Alves and P. M. Catarino, Relacoes Bidimensiona is E Identidades Da Sequencia De Leonardo, Revista Sergipana de Matematica e Educacao Matematica, No. 2 (2019), 156-173.
There are 11 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Yasemin Alp

E. Gökçen Koçer 0000-0002-7154-9063

Publication Date April 28, 2021
Submission Date December 27, 2020
Acceptance Date March 27, 2021
Published in Issue Year 2021 Volume: 9 Issue: 1

Cite

APA Alp, Y., & Koçer, E. G. (2021). Some Properties of Leonardo Numbers. Konuralp Journal of Mathematics, 9(1), 183-189.
AMA Alp Y, Koçer EG. Some Properties of Leonardo Numbers. Konuralp J. Math. April 2021;9(1):183-189.
Chicago Alp, Yasemin, and E. Gökçen Koçer. “Some Properties of Leonardo Numbers”. Konuralp Journal of Mathematics 9, no. 1 (April 2021): 183-89.
EndNote Alp Y, Koçer EG (April 1, 2021) Some Properties of Leonardo Numbers. Konuralp Journal of Mathematics 9 1 183–189.
IEEE Y. Alp and E. G. Koçer, “Some Properties of Leonardo Numbers”, Konuralp J. Math., vol. 9, no. 1, pp. 183–189, 2021.
ISNAD Alp, Yasemin - Koçer, E. Gökçen. “Some Properties of Leonardo Numbers”. Konuralp Journal of Mathematics 9/1 (April 2021), 183-189.
JAMA Alp Y, Koçer EG. Some Properties of Leonardo Numbers. Konuralp J. Math. 2021;9:183–189.
MLA Alp, Yasemin and E. Gökçen Koçer. “Some Properties of Leonardo Numbers”. Konuralp Journal of Mathematics, vol. 9, no. 1, 2021, pp. 183-9.
Vancouver Alp Y, Koçer EG. Some Properties of Leonardo Numbers. Konuralp J. Math. 2021;9(1):183-9.
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