Open AccessA STUDY ON THE SUMS OF SQUARES OF GENERALIZED TRIBONACCI NUMBERS: CLOSED FORM FORMULAS OF ∑_{k=0}ⁿkx^{k}W_{k}²
Author(s) -
Yüksel Soykan
Publication year - 2021
Publication title -
health sciences quarterly
Language(s) - English
Resource type - Journals
ISSN - 2791-6022
DOI - 10.26900/jsp.5.1.02
Subject(s) - mathematics , order (exchange) , combinatorics , least squares function approximation , statistics , economics , finance , estimator
In this paper, closed forms of the sum formulas ∑_{k=0}ⁿkx^{k}W_{k}², ∑_{k=0}ⁿkx^{k}W_{k+2}W_{k} and ∑_{k=0ⁿkx^{k}W_{k+1}W_{k} for the squares of generalized Tribonacci numbers are presented. 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.