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

Let n⩾3n⩾3 and let Jn≔circ(J1,J2,…,Jn)Jn≔circ(J1,J2,…,Jn) and jn≔circ(j0,j1,…,jn-1)jn≔circ(j0,j1,…,jn-1) be the n×nn×n circulant matrices associated with the Jacobsthal numbers J1,…,JnJ1,…,Jn and the Jacobsthal–Lucas numbers j0,…,jn-1j0,…,jn-1, respectively. The determinants and the inverses of JnJn and jnjn are obtained in terms of J1,…,JnJ1,…,Jn and j1,…,jn-1j1,…,jn-1, respectively.