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The Representation, Generalized Binet Formula and Sums of The Generalized Jacobsthal p-Sequence Correspondence to matrix theory has played an important and effective role. Quite apart from pursuing the discovery of the additional formulas by the matrix technics, the different matrices for obtaining new results can be introduced. Chen and Louck have investigated an nxn companion matrix and shown the combinatorial representation of the sequence generated by the nth power of the matrix [6]. Considering the matrix theory, Koken and Bozkurt have presented the Jacobsthal F-matrix and some results [7]. In the literature, there exist many other references on the subject which are not given here.The object of this article is to give a new definition for the generalization of the usual Jacobsthal sequence. The generating matrix, the Binet formula, characteristic equations, generating functions, combinatorial representations and sums of the terms of the generalized Jacobsthal sequence are respectively studied. Generalized Jacobsthal p-sequence Generalization of Jacobsthal SequenceFirst of all, the generalization of the usual Jacobsthal sequence is denoted by J p (n) and defined as follows: for p Z + and n > p+1,

According to the principle of the three-dimensional linearized theory of elastic waves in initially stressed bodies, a dynamical stress field in a pre-stressed bi-layered plate-strip under the action of an arbitrary inclined force resting on a rigid foundation is studied. It is assumed that the force applied to upper free surface of the plate-strip is time-harmonic and the materials used are linearly elastic, homogenous, and isotropic. By employing finite element method, the governing system of partial differential equations of motion is approximately solved. The different dependencies of the problem such as the ratio of height of plates and initial stress of the materials are numerically investigated. Particularly the effect of arbitrary inclined force is analyzed. It is observed that the numerical results obtained according to various angles converge to the ones in the previous studies.

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