Araştırma Makalesi
BibTex RIS Kaynak Göster

Some Properties of the Generalized Leonardo Numbers

Yıl 2024, Sayı: 47, 52 - 60, 30.06.2024
https://doi.org/10.53570/jnt.1470097

Öz

In this study, various properties of the generalized Leonardo numbers, which are one of the generalizations of Leonardo numbers, have been investigated. Additionally, some identities among the generalized Leonardo numbers have been obtained. Furthermore, some identities between Fibonacci numbers and generalized Leonardo numbers have been provided. In the last part of the study, binomial sums of generalized Leonardo numbers have been derived. The results obtained for generalized Leonardo numbers are reduced to Leonardo numbers.

Kaynakça

  • E. Lucas, Theorie des fonctions numeriques simplement periodiques, American Journal of Mathematics 1 (1878) 184-196.
  • V. E. Hoggatt, Jr., Fibonacci and Lucas numbers, Fibonacci Association, Santa Clara, 1969.
  • A. F. Horadam, A generalized Fibonacci sequence, American Mathematical Monthly 68 (1961) 455-459.
  • D. Kalman, R. Mena, The Fibonacci numbers-exposed, Mathematics Magazine 76 (3) (2003) 167-181.
  • T. Koshy, Fibonacci and Lucas numbers with applications, John Wiley and Sons, New York, 2001.
  • S. Vajda, Fibonacci and Lucas numbers and the golden section: Theory and applications, Halsted Press, Chichester, 1989.
  • P. M. M. C. Catarino, A. Borges, On Leonardo numbers, Acta Mathematica Universitatis Comenianae 89 (1) (2019) 75-86.
  • Y. Alp, E. G. Kocer, Some properties of Leonardo numbers, Konuralp Journal Mathematics 9 (1) (2021) 183-189.
  • U. Bednarz, M. Wołowiec-Musiał, Generalized Fibonacci–Leonardo numbers, Journal of Difference Equations and Applications 30 (1) (2024) 111-121.
  • P. M. M. C. Catarino, A. Borges, A note on incomplete Leonardo numbers, Integers: Electronic Journal of Combinatorial Number Theory 20 (2020) 1-7.
  • H. Gökbaş, A new family of number sequences: Leonardo-Alwyn numbers, Armenian Journal of Mathematics 15 (6) (2023) 1-13.
  • S. Halıcı, S. Curuk, On the Leonardo sequence via Pascal-type triangles, Journal of Mathematics 2024 (2024) Article ID 9352986 8 pages.
  • K. Kuhapatanakul, J. Chobsorn, On the generalized Leonardo numbers, Integers 22 (2022) #A48 7 pages.
  • M. Kumari, K. Prasad, H. Mahato, P. M. M. C. Catarino, On the generalized Leonardo quaternions and associated spinors, Kragujevac Journal of Mathematics 50 (3) (2026) 425-438.
  • K. Prasad, R. Mohanty, M. Kumari, H. Mahato, Some new families of generalized k-Leonardo and Gaussian Leonardo numbers, Communications in Combinatorics and Optimization 9 (2024) 539-553.
  • A. G. Shannon, A note on generalized Leonardo numbers, Notes on Number Theory and Discrete Mathematics 25 (3) (2019) 97-101.
  • A. G. Shannon, Ö. Deveci, A note on generalized and extended Leonardo sequences, Notes on Number Theory and Discrete Mathematics 28 (1) (2022) 109-114.
  • M. Shattuck, Combinatorial proofs of identities for the generalized Leonardo numbers, Notes on Number Theory and Discrete Mathematics 28 (24) (2022) 778-790.
  • E. Tan, H. H. Leung, On Leonardo p-numbers, Integers 23 (2023) #A7 11 pages.
  • N. J. A. Sloane, The On-Line Encyclopedia of Integer Sequences (2003), http://oeis.org, Accessed 24 Dec 2003.
Yıl 2024, Sayı: 47, 52 - 60, 30.06.2024
https://doi.org/10.53570/jnt.1470097

Öz

Kaynakça

  • E. Lucas, Theorie des fonctions numeriques simplement periodiques, American Journal of Mathematics 1 (1878) 184-196.
  • V. E. Hoggatt, Jr., Fibonacci and Lucas numbers, Fibonacci Association, Santa Clara, 1969.
  • A. F. Horadam, A generalized Fibonacci sequence, American Mathematical Monthly 68 (1961) 455-459.
  • D. Kalman, R. Mena, The Fibonacci numbers-exposed, Mathematics Magazine 76 (3) (2003) 167-181.
  • T. Koshy, Fibonacci and Lucas numbers with applications, John Wiley and Sons, New York, 2001.
  • S. Vajda, Fibonacci and Lucas numbers and the golden section: Theory and applications, Halsted Press, Chichester, 1989.
  • P. M. M. C. Catarino, A. Borges, On Leonardo numbers, Acta Mathematica Universitatis Comenianae 89 (1) (2019) 75-86.
  • Y. Alp, E. G. Kocer, Some properties of Leonardo numbers, Konuralp Journal Mathematics 9 (1) (2021) 183-189.
  • U. Bednarz, M. Wołowiec-Musiał, Generalized Fibonacci–Leonardo numbers, Journal of Difference Equations and Applications 30 (1) (2024) 111-121.
  • P. M. M. C. Catarino, A. Borges, A note on incomplete Leonardo numbers, Integers: Electronic Journal of Combinatorial Number Theory 20 (2020) 1-7.
  • H. Gökbaş, A new family of number sequences: Leonardo-Alwyn numbers, Armenian Journal of Mathematics 15 (6) (2023) 1-13.
  • S. Halıcı, S. Curuk, On the Leonardo sequence via Pascal-type triangles, Journal of Mathematics 2024 (2024) Article ID 9352986 8 pages.
  • K. Kuhapatanakul, J. Chobsorn, On the generalized Leonardo numbers, Integers 22 (2022) #A48 7 pages.
  • M. Kumari, K. Prasad, H. Mahato, P. M. M. C. Catarino, On the generalized Leonardo quaternions and associated spinors, Kragujevac Journal of Mathematics 50 (3) (2026) 425-438.
  • K. Prasad, R. Mohanty, M. Kumari, H. Mahato, Some new families of generalized k-Leonardo and Gaussian Leonardo numbers, Communications in Combinatorics and Optimization 9 (2024) 539-553.
  • A. G. Shannon, A note on generalized Leonardo numbers, Notes on Number Theory and Discrete Mathematics 25 (3) (2019) 97-101.
  • A. G. Shannon, Ö. Deveci, A note on generalized and extended Leonardo sequences, Notes on Number Theory and Discrete Mathematics 28 (1) (2022) 109-114.
  • M. Shattuck, Combinatorial proofs of identities for the generalized Leonardo numbers, Notes on Number Theory and Discrete Mathematics 28 (24) (2022) 778-790.
  • E. Tan, H. H. Leung, On Leonardo p-numbers, Integers 23 (2023) #A7 11 pages.
  • N. J. A. Sloane, The On-Line Encyclopedia of Integer Sequences (2003), http://oeis.org, Accessed 24 Dec 2003.
Toplam 20 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Cebir ve Sayı Teorisi
Bölüm Araştırma Makalesi
Yazarlar

Yasemin Alp 0000-0002-4146-7374

Yayımlanma Tarihi 30 Haziran 2024
Gönderilme Tarihi 17 Nisan 2024
Kabul Tarihi 30 Mayıs 2024
Yayımlandığı Sayı Yıl 2024 Sayı: 47

Kaynak Göster

APA Alp, Y. (2024). Some Properties of the Generalized Leonardo Numbers. Journal of New Theory(47), 52-60. https://doi.org/10.53570/jnt.1470097
AMA Alp Y. Some Properties of the Generalized Leonardo Numbers. JNT. Haziran 2024;(47):52-60. doi:10.53570/jnt.1470097
Chicago Alp, Yasemin. “Some Properties of the Generalized Leonardo Numbers”. Journal of New Theory, sy. 47 (Haziran 2024): 52-60. https://doi.org/10.53570/jnt.1470097.
EndNote Alp Y (01 Haziran 2024) Some Properties of the Generalized Leonardo Numbers. Journal of New Theory 47 52–60.
IEEE Y. Alp, “Some Properties of the Generalized Leonardo Numbers”, JNT, sy. 47, ss. 52–60, Haziran 2024, doi: 10.53570/jnt.1470097.
ISNAD Alp, Yasemin. “Some Properties of the Generalized Leonardo Numbers”. Journal of New Theory 47 (Haziran 2024), 52-60. https://doi.org/10.53570/jnt.1470097.
JAMA Alp Y. Some Properties of the Generalized Leonardo Numbers. JNT. 2024;:52–60.
MLA Alp, Yasemin. “Some Properties of the Generalized Leonardo Numbers”. Journal of New Theory, sy. 47, 2024, ss. 52-60, doi:10.53570/jnt.1470097.
Vancouver Alp Y. Some Properties of the Generalized Leonardo Numbers. JNT. 2024(47):52-60.


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