A Study on Sum Formulas of Generalized Tetranacci Numbers: Closed Forms of the Sum Formulas \(\sum_{k=0}^{n}kW_{k}\) and \(\sum_{k=1}^{n}kW_{-k}\)
Y¨ uksel Soykan *
Department of Mathematics, Faculty of Art and Science, Zonguldak B¨ ulent Ecevit University, 67100, Zonguldak, Turkey.
*Author to whom correspondence should be addressed.
Abstract
In this paper, closed forms of the sum formulas \(\sum_{k=0}^{n}kW_{k}\) and \(\sum_{k=1}^{n}kW_{-k}\) for generalized Tetranacci numbers are presented. As special cases, we give summation formulas of Tetranacci, Tetranacci-Lucas, and other fourth-order recurrence sequences.
Keywords: Tetranacci numbers, Tetranacci-Lucas numbers, fourth order Pell numbers, sum formulas, summing formulas.