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

Authors : Yüksel SOYKAN

Pages : 1-23

Doi:10.26900/jsp.5.1.02

View : 8 | Download : 4

Publication Date : 2021-02-15

Article Type : Research Paper

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