Matrix Representation of an All-inclusive Fibonacci Sequence

Background and Objective: Fibonacci sequence is a sequence of positive integers that has been studied over several years. The aim of this paper was to suggest new generalized Fibonacci sequence to a particular class of recursive sequence. Materials and Methods: The equilibrium point of the model was investigated and a new sequence. The matrix method was applied to perform the generalization. Results: The nth power of the generating matrix for this generalized Fibonacci sequence was established and some basic properties of this sequence were obtained by matrix methods. Conclusion: Cassinis identity and Binets formula for the generalized Fibonacci sequence was obtained.