Let n ≥ 3 and Jn := circ(J1, J2, . . . , Jn) and גn := circ(j0, j1, . . . , jn−1) be the n × n circulant matrices, associated with the nth Jacobsthal number Jn and the nth Jacobsthal-Lucas number jn, respectively. The determinants of Jn and גn are obtained in terms of the Jacobsthal and Jacobsthal-Lucas numbers. These imply that Jn and גn are invertible. We also derive the inverses of Jn and גn), i.e., where J k and j k are the kth Jacobsthal and Jacobsthal-Lucas numbers, respectively, with the recurrence relations J k = J k−1 + 2J k−2 , j k = j k−1 + 2j k−2 , and the initial conditions J 0 = 0, J 1 = 1, j 0 = 2, and j 1 = 1 (k ≥ 2). Let α and β be
In this paper, we investigate the Pell sequence and the Perrin sequence and we derive some relationships between these sequences and permanents and determinants of one type of Hessenberg matrices.
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