Shahid Bahonar University of Kerman Journal of Mahani Mathematical Research 2251-7952 12 2 2023 05 01 A note on sum formulas $\sum_{k=0}^{n}kx^{k}W_{k}$ and $\sum_{k=1}^{n}kx^{k}W_{-k}$ of generalized Hexanacci numbers 137 164 3408 10.22103/jmmr.2022.19594.1273 EN Yuksel Soykan Department of Mathematics, Art and Science Faculty, Zonguldak Bulent Ecevit University, Zonguldak, Turkey 0000-0002-1895-211X Erkan Taşdemir Pinarhisar Vocational School, Kirklareli University, Kirklareli, Turkey 0000-0002-5002-3193 Tulin Erdoğan Taşdemir Ministry of National Education, Pinarhisar Anatolian High School, Kirklareli, Turkey 0000-0002-7333-0217 Journal Article 2022 06 01 In this paper, closed forms of the sum formulas $ \sum_{k=0}^{n}kx^{k}W_{k} $ and $ \sum_{k=1}^{n} kx^{k}W_{- k} $ for generalized Hexanacci numbers are presented. As special cases, we give summation formulas of Hexanacci, Hexanacci-Lucas, and other sixth-order recurrence sequences. https://jmmrc.uk.ac.ir/article_3408_734e6bfcd358e25ac1db0a4241b95651.pdf