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

How to Cite?: Mansi N. Zaveri, Dr. Jayant K. Patel, "Binets Formula for the Tetranacci Sequence", Volume 5 Issue 12, December 2016, International Journal of Science and Research (IJSR), Pages: 1911-1913, https://www.ijsr.net/getabstract.php?paperid=ART20163927, DOI: https://dx.doi.org/10.21275/ART20163927

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