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}

  • Yüksel Soykan Department of Mathematics, Art and Science Faculty, Zonguldak Bulent Ecevit University, 67100, Zonguldak, Turkey
Keywords: Tribonacci numbers, Padovan numbers, Perrin numbers, sum formulas

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.

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Published
2020-10-22
How to Cite
Soykan, Y. (2020). 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}. Journal of Progressive Research in Mathematics, 17(1), 1-40. Retrieved from http://scitecresearch.com/journals/index.php/jprm/article/view/1934
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Articles