On the generalization of third order linear recurrence relations and matrix representation

In this paper, generalization Vₙ( Vᵢ,pᵢ )=∑ⱼ₌₁³p₁Vₙ₋ⱼ, j=1,2,3, n≥ 4 of the third order linear recurrence relations is considered and represented in two different ways to generate Tribonacci numbers. Thereby, a matrix representation is established to engender numbers and to investigate identities and results in the generalized form. It is observed from the obtained generalized results that relevant previous outcomes become the special cases. On picking up Vⱼ,pⱼ, j=1,2,3 initial terms, coefficients of the linear recurrence relations and the power n of the matrixMⁿ arbitrarily, to demonstrate the communication of message. For secruty, same message can be send frequently with a different paprmetres by varying Vⱼ,pⱼ, j=1,2,3 and n . A numerical example is presented to illustrate to forward and retrieve the messages.