Abstract
In this study, we first give the definitions of (s,t)-Jacobsthal and (s,t)-Jacobsthal Lucas sequence. By using these formulas we define (s,t)-Jacobsthal and (s,t)-Jacobsthal Lucas matrix sequences. After that we establish some sum formulas for these matrix sequences.
Highlights
There are so many studies in the literature that are concern about special number sequences such as Fibonacci, Lucas, Pell, Jacobsthal, and Padovan in [1] [2]
Jacobsthal and Jacobsthal Lucas numbers are given by the recurrence relations jn = jn−1 + 2 jn−2, j0 = 0, j1 = 1 and cn = cn−1 + 2cn−2, c0 = 2, c1 = 1 for n ≥ 2, respectively in [7]-[9]
Uygun defined ( s, t ) Jacosthal and ( s, t ) Jacosthal Lucas matrix sequences and by using them found some properties of Jacobsthal numbers in [17]
Summary
There are so many studies in the literature that are concern about special number sequences such as Fibonacci, Lucas, Pell, Jacobsthal, and Padovan in [1] [2]. They are widely used in many research areas as Engineering, Architecture, Nature and Art in [3]-[6]. Turkmen defined ( s, t ) Fibonacci and ( s, t ) Lucas matrix sequences in [15] [16]. Uygun defined ( s, t ) Jacosthal and ( s, t ) Jacosthal Lucas matrix sequences and by using them found some properties of Jacobsthal numbers in [17]. 2. The (s,t)-Jacobsthal matrix sequence are defined by the recurrence relations and (s,t)-Jacobsthal Lucas matrix sequence. For their proofs you can look at the Ref. [17]
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