New Recurrence Relations for Tribonacci Sequence and Generalized Tribonacci Sequence

Authors

  • Engin ÖZKAN Erzincan BinaliYıldırım University
  • Songül ÇELİK
  • İnan DURUKAN

DOI:

https://doi.org/10.37591/rrdms.v7i3.2616

Keywords:

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

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 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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Published

2021-01-16

Issue

Vol. 7 No. 3 (2020)

Section

Research Articles

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