Tribonacci Sayıları ile İlişkili Bir Tamsayı Dizisininin Genellemesi

Öz

Bu çalışmada önce {1,2, . . . ,n } kümesinin ardışık üç tek sayı içermeyen S alt kümelerinin sayısına karşılık gelen tam sayı dizisini göz önüne aldık. Sonra bu diziyi, Tribonacci polinomları ile ilişkili bir polinom dizisine genelledik. Daha sonar polinom dizisinin bazı temel özelliklerini elde ettik.

Anahtar Kelimeler

• Polinom dizileri
• Tribonacci polinomları
• Ardışık tek sayılar
• Üreteç fonksiyon

Generalization of an Integer Sequence Associated with Tribonacci Numbers

Öz

In this paper we first consider an integer sequence which enumerates the number of subsets of S of the set [n]={1,2, . . . ,n } containing no three consecutive odd integers. Then we generalize this sequence to a polynomial sequence which is associated with the Tribonacci polynomials. Next, we obtain some basic properties of the polynomial sequence.

Anahtar Kelimeler

• Polynomial sequence
• Tribonacci polynomials
• Consecutive odd integers
• Generating function

Kaynakça

1. Arslan, B. and Uslu, K. (2021). Number of Subsets of the Set [n] Including No Three Consecutive Odd Integers, European Journal of Science and Technology, (28), pp. 352-356.
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3. Hoggatt V. E. and Bicknell, M. (1973). Generalized Fibonacci polynomials, Fibonacci Quarterly, Vol. 11, pp. 457–465.
4. Kocer E. G. and Gedikli, H. (2016). Trivariate Fibonacci and Lucas polynomials,’’ Konuralp J. Math., 4, pp. 247–254.
5. Koshy, T. (2011). Fibonacci and Lucas Numbers with Applications, Wiley Interscience Publications, New York.
6. Ramirez, J. L. and Sirvent, V. F. (2014). Incomplete Tribonacci Numbers and Polynomials, Journal of Integer Sequences, 17, Article 14.4.2.
7. Rybołowicz, B. & Tereszkiewicz, A. (2018). Generalized Tricobsthal and generalized Tribonacci polynomials,” Applied Mathematics and Computation, 325, pp. 297–308.
8. Yilmaz, N. and Taskara, N. (2014). Incomplete Tribonacci–Lucas Numbers and Polynomials.’’ Advances in Applied Clifford Algebras, 25, pp. 741-753.

9. 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.