Open AccessOn the Sums of Squares of Generalized Tribonacci Numbers: Closed Formulas of Σn k=0 xkW2
Author(s) -
Yüksel Soykan
Publication year - 2020
Publication title -
archives of current research international
Language(s) - English
Resource type - Journals
ISSN - 2454-7077
DOI - 10.9734/acri/2020/v20i430187
Subject(s) - mathematical proof , mathematics , order (exchange) , combinatorics , least squares function approximation , recurrence relation , statistics , geometry , finance , estimator , economics
In this paper, closed forms of the sum formulas Σn k=0 xkW2 k ; Σn k=0 xk Σ Wk+1Wk and n k=0 xkWk+2Wk 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. We present the proofs to indicate how these formulas, in general, were discovered. Of course, all the listed formulas may be proved by induction, but that method of proof gives no clue about their discovery. Our work generalize third order recurrence relations.