A STUDY ON THE SUMS OF SQUARES OF GENERALIZED TRIBONACCI NUMBERS: CLOSED FORM FORMULAS OF ∑_{k=0}ⁿkx^{k}W_{k}²
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https://doi.org/10.26900/jsp.5.1.02Keywords:
Sums of squares, third order recurrence,, generalized Tribonacci numbers, Padovan numbers , Perrin numbers, Narayana numbersAbstract
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.
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