New Recurrence Relations for Tribonacci Sequence and Generalized Tribonacci Sequence

Abstract

Abstract

Tribonacci numbers are placed on the corners of polygons clockwise with each corner receiving a term. Then, it is argued whether there is a relationship among the numbers in the same corners. It is shown to be able to find m^th term corresponding to the corner A_k in an n-gon by a relation:

where,  is a Tribonaccisequence and  is a Tribonacci- Lucas sequence. The relation is proved by using a binet formula obtained for . It is also argued whether the relation corrects all Generalized Tribonacci sequences by changing the beginning terms. Moreover, it is shown that m^th term corresponding to the corner A_k in an n-gon can be found by using the following relation:

Keywords: Binet formula, Fibonacci Sequences, n-gon, Tribonacci Numbers, Tribonacci-Lucas Numbers