A Study on Sum Formulas for Generalized Tribonacci Numbers: Closed Forms of the Sum Formulas ∑_{k=0}ⁿkx^{k}W_{k}, ∑_{k=1}ⁿkx^{k}W_{-k}

Abstract

In this paper, closed forms of the sum formulas ∑_{k=0}ⁿkx^{k}W_{k}, ∑_{k=1}ⁿkx^{k}W_{-k} for generalized Tribonacci numbers are presented. As special cases, we give summation formulas of Tribonacci, Tribonacci-Lucas, Padovan, Perrin, Narayana and some other third order linear recurrance sequences