Abstract: The concept of generalized Jacobsthal sequence of order k is introduced. The generating function of Jacobsthal sequence of order k and the related combinatorial identities are obtained. The enumerations of two classes of lattice paths are studied and the two combinatorial interpretations of Jacobsthal numbers of order k are given.

Key words: Jacobsthal number, Jacobsthal sequence of order k, Riordan array, generating function, lattice path A-matrix