Öz
This study introduces the generalized Francois numbers and investigates their some properties. In addition, we give the basic formulas such as Binet's formula, sums formulas. Also, we provide some identities among the Fibonacci sequence, the Lucas sequence, and the generalized Francois sequence.
Anahtar Kelimeler
Binet’s formula Fibonacci numbers Francois numbers Lucas numbers Leonardo numbers.
Kaynakça
- Alp, Y., Kocer, E.G., Some properties of Lenardo numbers, Konuralp J. Math., 9(1)(2021), 183–189.
- Catarino, P., Borges, A., On Leonardo numbers, Acta Math. Univ. Comenian, 89(1) (2019), 75–86.
- Diskaya, O., Menken, H., Catarino, P., On the hyperbolic Leonardo and hyperbolic Francois quaternions, Journal of New Theory, 42(2023)(2023), 74–85.
- Gökbaş, H., A new family of number sequences: Leonardo-Alwyn numbers, Armenian Journal of Mathematics, 15(6)(2023), 1–13.
- Koshy, T., Fibonacci and Lucas Numbers with Applications, John Wiley&Sons, 2001.
- Kuhapatanakul, K., Chobsorn, J., On the generalized Leonardo numbers, Integers, 22(2022), A48.
- Kumari, M., Prasad, K., Mahato, H., Catarino, P.M.M., On the generalized Leonardo quaternions and associated spinors, Kragujevac Journal of Mathematics, 50(3)(2026), 425–438.
- Cerda-Morales, G., Introduction to generalized Leonardo-Alwyn hybrid numbers, (2024), arXiv:2405.13074.
- Saçlı, G.Y., Yüce, S., A note on hyper-dual numbers with the Leonardo-Alwyn sequence, Turkish Journal of Mathematics and Computer Science, 16(1)(2024), 154–161.
- Savin, D., Tan, E., On Companion sequences associated with Leonardo quaternions: Applications over finite fields, (2024), arXiv:2403.01592.
- Shannon, A.G., A note on generalized Leonardo numbers, Notes on Number Theory and Discrete Mathematics, 25(3)(2019), 97–101.
- Shattuck, M., Combinatorial proofs of identities for the generalized Leonardo numbers, Notes on Number Theory and Discrete Mathematics, 28(24)(2022), 778–790.
- Sloane, N.J.A., The On-Line Encyclopedia of Integer Sequences, http://oeis.org.
- Vajda, S., Fibonacci and Lucas Numbers and the Golden Section: Theory and Applications, Halsted Press, 1989.
- Yilmaz, Ç.Z., Saçlı, G.Y., On dual quaternions with k-generalized Leonardo components, Journal of New Theory, 44(2023), 31–42.
Öz
Kaynakça
- Alp, Y., Kocer, E.G., Some properties of Lenardo numbers, Konuralp J. Math., 9(1)(2021), 183–189.
- Catarino, P., Borges, A., On Leonardo numbers, Acta Math. Univ. Comenian, 89(1) (2019), 75–86.
- Diskaya, O., Menken, H., Catarino, P., On the hyperbolic Leonardo and hyperbolic Francois quaternions, Journal of New Theory, 42(2023)(2023), 74–85.
- Gökbaş, H., A new family of number sequences: Leonardo-Alwyn numbers, Armenian Journal of Mathematics, 15(6)(2023), 1–13.
- Koshy, T., Fibonacci and Lucas Numbers with Applications, John Wiley&Sons, 2001.
- Kuhapatanakul, K., Chobsorn, J., On the generalized Leonardo numbers, Integers, 22(2022), A48.
- Kumari, M., Prasad, K., Mahato, H., Catarino, P.M.M., On the generalized Leonardo quaternions and associated spinors, Kragujevac Journal of Mathematics, 50(3)(2026), 425–438.
- Cerda-Morales, G., Introduction to generalized Leonardo-Alwyn hybrid numbers, (2024), arXiv:2405.13074.
- Saçlı, G.Y., Yüce, S., A note on hyper-dual numbers with the Leonardo-Alwyn sequence, Turkish Journal of Mathematics and Computer Science, 16(1)(2024), 154–161.
- Savin, D., Tan, E., On Companion sequences associated with Leonardo quaternions: Applications over finite fields, (2024), arXiv:2403.01592.
- Shannon, A.G., A note on generalized Leonardo numbers, Notes on Number Theory and Discrete Mathematics, 25(3)(2019), 97–101.
- Shattuck, M., Combinatorial proofs of identities for the generalized Leonardo numbers, Notes on Number Theory and Discrete Mathematics, 28(24)(2022), 778–790.
- Sloane, N.J.A., The On-Line Encyclopedia of Integer Sequences, http://oeis.org.
- Vajda, S., Fibonacci and Lucas Numbers and the Golden Section: Theory and Applications, Halsted Press, 1989.
- Yilmaz, Ç.Z., Saçlı, G.Y., On dual quaternions with k-generalized Leonardo components, Journal of New Theory, 44(2023), 31–42.
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Konular | Cebir ve Sayı Teorisi |
| Bölüm | Makaleler |
| Yazarlar | |
| Yayımlanma Tarihi | 31 Aralık 2024 |
| Gönderilme Tarihi | 3 Nisan 2024 |
| Kabul Tarihi | 2 Ekim 2024 |
| Yayımlandığı Sayı | Yıl 2024 Cilt: 16 Sayı: 2 |