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

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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