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Research & Reviews: Discrete Mathematical Structures

New Recurrence Relations for Tribonacci Sequence and Generalized Tribonacci Sequence

  1. Engin ÖZKAN
  2. Songül ÇELİK
  3. İnan DURUKAN

Abstract

AbstractTribonacci 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 mth term corresponding to the corner Ak 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 mth term corresponding to the corner Ak in an n-gon can be found by using the following relation: Keywords: Binet formula, Fibonacci Sequences, n-gon, Tribonacci Numbers, Tribonacci-Lucas Numbers

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