In this study, we investigate the form of the solutions of the following rational difference equation systems 1 1 1      such that their solutions are associated with Padovan numbers.

In this study, we investigate the solutions of two special types of the Riccati difference equation x n+1 = 1 1+x n and y n+1 = 1 -1+y n such that their solutions are associated with Fibonacci numbers.

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.

In this paper, we present new upper and lower bounds for the spectral norm of an

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