Binets Formula for the Tetranacci Sequence

Mansi N. Zaveri, Dr. Jayant K. Patel

Abstract: In this paper, we derive an analog of Binets formula for the Tetranacci sequence with initial terms t_0=t_1=t_2=0 & t_3=1 and with recurrence relation t_n=t_ (n-1) +t_ (n-2) +t_ (n-3) +t_ (n-4), n4. This formula gives t_n explicitly as a function of index n and the roots of the associated characteristic equation x^4-x^3-x^2-x-1=0. In this study we also prove that the ratio of two terms T_ (n + i) and T_ (n) of the generalized Tetranacci sequence approaches the value ^ (i) as n tends to infinity. where, is the Tetranacci constant.

Keywords: Tetranacci sequence, Tetranacci numbers, Binets formula Generalized Tetranacci Sequence, Tetranacci Constant