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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