Öz
Tribonacci polinom dizileri Tribonacci sayılarının bir genişlemesidir. {1, 2, . . . ,n } kümesinin ardışık üç çift tam sayı içermeyen S alt kümelerinin sayısını veren tam sayı dizisini göz önüne aldık. Bu tamsayı dizisini genelleyen bir polinom dizisi tanımladık. Polinom dizisi Tribonacci polinomları ile ilişkilendirildi. Bu polinom dizisinin kapalı formülünü bulduk ve polinom dizisinin bazı temel özelliklerini elde ettik.
Anahtar Kelimeler
Tribonacci sayıları Tribonacci polinomları Polinom dizisi Ardışık çift sayılar Üreteç fonksiyon
Kaynakça
- Arslan, B. and Uslu, K. (2021). Number of Subsets of the Set [n] Including No Three Consecutive Even Integers, European Journal of Science and Technology, (28), pp. 552-556.
- Bueno, A. C. F. (2015). A note on generalized Tribonacci sequence, Notes on Number Theory and Discrete Mathematics, 21, pp. 67-69.
- Hoggatt V. E. and Bicknell, M. (1973). Generalized Fibonacci polynomials, Fibonacci Quarterly, Vol. 11, pp. 457–465.
- Kocer E. G. and Gedikli, H. (2016). Trivariate Fibonacci and Lucas polynomials,’’ Konuralp J. Math., 4, pp. 247–254.
- Koshy, T. (2011). Fibonacci and Lucas Numbers with Applications, Wiley Interscience Publications, New York.
- Ramirez, J. L. and Sirvent, V. F. (2014). Incomplete Tribonacci Numbers and Polynomials, Journal of Integer Sequences,17, Article 14.4.2.
- Rybołowicz, B. & Tereszkiewicz, A. (2018). Generalized Tricobsthal and generalized Tribonacci polynomials,” Applied Mathematics and Computation, 325, pp. 297–308.
- Yilmaz, N. and Taskara, N. (2014). Incomplete Tribonacci–Lucas Numbers and Polynomials.’’ Advances in Applied Clifford Algebras, 25, pp. 741-753.
- Yogesh Kumar Gupta, Badshah, V. H., Mamta Singh, Kiran Sisodiya. (2016). Some Identities of Tribonacci Polynomials, Turkish Journal of Analysis and Number Theory. Vol. 4, No. 1, pp. 20-22.
Öz
Tribonacci polynomial sequence is an extension of Tribonacci numbers. We consider an integer sequence enumerating the number of subsets of S of the set [n]={1,2, . . . ,n } containing no three consecutive even integers. We define a polynomial sequence generalizing this integer sequence. The polynomial sequence is associated with the Tribonacci polynomials. We find the closed form formula and derive some basic properties of the polynomial sequence.
Anahtar Kelimeler
Tribonacci sayıları Tribonacci polinomları Polinom dizisi Ardışık çift sayılar Üreteç fonksiyon
Kaynakça
- Arslan, B. and Uslu, K. (2021). Number of Subsets of the Set [n] Including No Three Consecutive Even Integers, European Journal of Science and Technology, (28), pp. 552-556.
- Bueno, A. C. F. (2015). A note on generalized Tribonacci sequence, Notes on Number Theory and Discrete Mathematics, 21, pp. 67-69.
- Hoggatt V. E. and Bicknell, M. (1973). Generalized Fibonacci polynomials, Fibonacci Quarterly, Vol. 11, pp. 457–465.
- Kocer E. G. and Gedikli, H. (2016). Trivariate Fibonacci and Lucas polynomials,’’ Konuralp J. Math., 4, pp. 247–254.
- Koshy, T. (2011). Fibonacci and Lucas Numbers with Applications, Wiley Interscience Publications, New York.
- Ramirez, J. L. and Sirvent, V. F. (2014). Incomplete Tribonacci Numbers and Polynomials, Journal of Integer Sequences,17, Article 14.4.2.
- Rybołowicz, B. & Tereszkiewicz, A. (2018). Generalized Tricobsthal and generalized Tribonacci polynomials,” Applied Mathematics and Computation, 325, pp. 297–308.
- Yilmaz, N. and Taskara, N. (2014). Incomplete Tribonacci–Lucas Numbers and Polynomials.’’ Advances in Applied Clifford Algebras, 25, pp. 741-753.
- Yogesh Kumar Gupta, Badshah, V. H., Mamta Singh, Kiran Sisodiya. (2016). Some Identities of Tribonacci Polynomials, Turkish Journal of Analysis and Number Theory. Vol. 4, No. 1, pp. 20-22.
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Konular | Mühendislik |
| Bölüm | Makaleler |
| Yazarlar | |
| Yayımlanma Tarihi | 31 Mayıs 2022 |
| Yayımlandığı Sayı | Yıl 2022 |