A Study On the Sums of Squares of Generalized Tribonacci Numbers: Closed Form Formulas of Pn k=0 kxkW2

Year 2021, Volume: 5 Issue: 1, 1 - 23, 15.02.2021

Yüksel Soykan

https://doi.org/10.26900/jsp.5.1.02

Abstract

In this paper, closed forms of the sum formulas
Pn
k=0 kxkWk
2;
Pn
k=0 kxkWk+2Wk and
Pn
k=0 kxkWk+1Wk
for the squares of generalized Tribonacci numbers are presented. Here, fWmgm2Z is the generalized Tribonacci se-
quence, n is a non-negative integer and x is a real or complex number. As special cases, we give summation formulas
of Tribonacci, Tribonacci-Lucas, Padovan, Perrin numbers and the other third order recurrence relations.
2020 Mathematics Subject Classication. 11B39, 11B83.

Keywords

Sums of squares , third order recurrence , generalized Tribonacci numbers , Padovan numbers , Perrin numbers , Narayana numbers

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