The Properties of Binomial Transforms for Modified (s,t)-Pell Matrix Sequence
Abstract
In this study, we investigate a generalization of the modified Pell sequence, which is called $(s,t)$-modified Pell sequence. By considering this sequence, we define the matrix sequence whose elements are $(s,t)$-modified Pell numbers. Furthermore, we define various binomial transforms for modified $ (s,t)$-Pell matrix sequence. Finally, we give some relationships for $(s,t)$-modified Pell matrix sequences such as Binet formulas, the generating functions, and some sum formulas.
Keywords
Binet formula, Binomial transforms, Generating function, Modified (s, t)-Pell sequence
References
- [1] S. Falcon, A. Plaza, Binomial transforms of the k-Fibonacci sequence, Int. J. Nonlinear Sci. Numer. Simul., 10(11-12) (2009), 1527-1538.
- [2] N. Yilmaz, N. Taskara, Binomial sransforms of the Padovan and Perrin matrix sequences, Abstr. Appl. Anal., 2013 (2013), Article ID 497418, 7 pages.
- [3] P. Bhadouria, D. Jhala, B. Singh, Binomial transforms of the k-Lucas sequence, J. Math. Comput. Sci., 8(1) (2014), 81-92.
- [4] S. Uygun, A. Erdo˘gdu, Binominal transforms of k-Jacobsthal sequences, J. Math. Comput. Sci., 7(6) (2017), 1100-1114.
- [5] C. Kızılateş, N. Tuglu, B. Çekim, Binomial transform of quadrapell sequences and quadrapell matrix sequences, J. Sci. Arts, 1(38) (2017), 69-80.
- [6] S. Uygun, The binomial transforms of the generalized (s; t) -Jacobsthal matrix sequence, Int. J. Adv. Appl. Math. Mech., 6(3) (2019), 14-20.
- [7] Y. Kwon, Binomial transforms of the modified k-Fibonacci-like sequence, Int. J. Math. Comput. Sci., 14(1) (2019), 47-59.
- [8] S. Uygun, Binominal transforms of k-Jacobsthal Lucas sequences, Rom. J. Math. Comput. Sci., 2(10) (2020), 43-54.
- [9] N. Yılmaz, Binomial transforms of the Balancing and Lucas-Balancingpolynomials, Contributions Discrete Math., 15(3) (2020), 133-144.
- [10] Y. Soykan, Binomial transform of the generalized tribonacci sequence, Asian Res. J. Math., 16(10) (2020), 26-55.
