Binet – Type Formula For The Sequence of Tetranacci Numbers by Alternate Methods

Abstract

The sequence {T_n} of Tetranacci numbers is defined by recurrence relation T_n= T_n-1 + T_n-2 + T_n-3 + T_n-4; n≥4 with initial condition T₀=T₁=T₂=0 and T₃=1. In this Paper, we obtain the explicit formulla-Binet-type formula for T_n by two different methods. We use the concept of Eigen decomposition as well as of generating functions to obtain the result.