Open AccessA Study on Generalized Fibonacci Numbers: Sum Formulas $\sum_{k=0}^{n}kx^{k}W_{k}^{3}$ and $\sum_{k=1}^{n}kx^{k}W_{-k}^{3}$ for the Cubes of Terms
Author(s) -
Yüksel Soykan
Publication year - 2020
Publication title -
earthline journal of mathematical sciences
Language(s) - English
Resource type - Journals
ISSN - 2581-8147
DOI - 10.34198/ejms.4220.297331
Subject(s) - fibonacci number , lucas number , combinatorics , mathematics , pisano period , lucas sequence , recurrence relation , fibonacci polynomials , discrete mathematics , orthogonal polynomials , difference polynomials
In this paper, closed forms of the sum formulas $\sum_{k=0}^{n}kx^{k}W_{k}^{3}$ and $\sum_{k=1}^{n}kx^{k}W_{-k}^{3}$ for the cubes of generalized Fibonacci numbers are presented. As special cases, we give sum formulas of Fibonacci, Lucas, Pell, Pell-Lucas, Jacobsthal, Jacobsthal-Lucas numbers.