Result: A study on the sum of the squares of generalized Balancing numbers: the sum formula $\sum_{k=0}^{n}x^{k}W_{mk+j}^{2}$

Title:
A study on the sum of the squares of generalized Balancing numbers: the sum formula $\sum_{k=0}^{n}x^{k}W_{mk+j}^{2}$
Authors:
Soykan, Yüksel, Taşdemir, Erkan, Dikmen, Can Murat
Source:
Journal of Innovative Applied Mathematics and Computational Sciences; Vol. 1 No. 1 (2021): July- December; 16-30 ; 2773-4196 ; 10.58205/jiamcs.v1i1 ; ark:/49935/jiamcs.v1i1
Publisher Information:
University Center Abdelhafid Boussouf of MILA, ALGERIA.
Publication Year:
2021
Subject Terms:
Balancing numbers, modified Lucas-balancing numbers, Lucas-balancing numbers, sum formulas, Recurrences, Fibonacci and Lucas numbers and polynomials and generalizations, Special sequences and polynomials
Document Type:
Academic journal article in journal/newspaper
File Description:
application/pdf
Language:
English
Relation:
https://jiamcs.centre-univ-mila.dz/index.php/jiamcs/article/view/v1i1_07/v1i1_07; ark:/49935/jiamcs.v1i1.7
DOI:
10.58205/jiamcs.v1i1.7
Availability:
https://jiamcs.centre-univ-mila.dz/index.php/jiamcs/article/view/v1i1_07
https://doi.org/10.58205/jiamcs.v1i1.7
Rights:
Copyright (c) 2021 Yüksel Soykan, Erkan Taşdemir, Can Murat Dikmen ; https://creativecommons.org/licenses/by-nc-nd/4.0
Accession Number:
edsbas.5E7BEFE
Database:
BASE

Further Information

In this paper, closed forms of the sum formulas $\sum_{k=0}^{n}x^{k}W_{mk+j}^{2}$ for generalized balancing numbers arepresented. As special cases, we give sum formulas of balancing, modified Lucas-balancing and Lucas-balancing numbers.