A New Like Fibonacci Sequence and Its Properties

Abstract

The Twin Fibonacci sequences are first defined and their linear expressions are given in this paper.The sequence{U_n} which is constituted by the matrix eigenvalues is defined and a discussion is given to its properties,including some exact division properties of the sequence{U_n} taken modulo m,and the theorem on the least period for module sequence{u_n(p^r)} is shown. Moreover,the relationship theorem between the module sequence of the sequence{U_n} about m and that for the Twin Fibonacci sequence is given in the paper,providing necessary mathematical support for further studying the properties of the Twin Fibonacci sequence.