Matrix Sequences in terms of Padovan and Perrin Numbers

Abstract

The first main idea of this paper is to develop thematrix sequencesthat represent Padovan and Perrin numbers. Then, by taking into account matrix properties of these new matrix sequences, some behaviours of Padovan and Perrin numbers will be investigated. Moreover, some important relationships between Padovan and Perrin matrix sequences will be presented.

The matrix sequence in terms of bi-periodic Fibonacci numbers

“…Yazlik et al,in [14], establish generalized (s, t)-matrix sequences and present some important relationships among (s, t)-Fibonacci and (s, t)-Lucas sequences and their matrix sequences. In [16], Yilmaz and Taskara defined the matrix sequences of Padovan and Perrin numbers. Then, they presented the relationships between these matrix sequences.…”

Matrix Sequences of Tetranacci and Tetranacci-Lucas Numbers

“…On the other hand, the matrix sequences have taken so much interest for di¤erent type of numbers. For matrix sequences of generalized Horadam type numbers, see for example [2], [3], [5], [15], [16], [17], [18], [23], and for matrix sequences of generalized Tribonacci type numbers, see for instance [1], [12], [13], [19], [20].…”

A note on the bi-periodic Fibonacci and Lucas matrix sequences

“…On the other hand, the matrix sequences have taken so much interest for different type of numbers ( [2,3,4,7,9,12,14,16]). In [4], the authors defined bi-periodic Fibonacci matrix sequence and obtained nth general term of this matrix sequence as…”