Determinants and inverses of circulant matrices with Jacobsthal and Jacobsthal-Lucas Numbers

Let n >= 3 and let J(n) := circ(J(1),J(2),...,J(n)) and j(n) := circ(j(0),j(1),...,j(n-1)) be the n x n circulant matrices associated with the Jacobsthal numbers J(1),...,J(n) and the Jacobsthal-Lucas numbers j(0),...,j(n-1), respectively. The determinants and the inverses of J(n) and j(n) are obtained in terms of J(1),...,J(n) and j(1),...,j(n-1), respectively. (C) 2012 Elsevier Inc. All rights reserved.