{"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":"Y. Soykan, E. Taşdemir, C. M. Dikmen","doi":"10.58205/jiamcs.v1i1.7","DOIUrl":null,"url":null,"abstract":"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.","PeriodicalId":289834,"journal":{"name":"Journal of Innovative Applied Mathematics and Computational Sciences","volume":"42 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2021-12-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Innovative Applied Mathematics and Computational Sciences","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.58205/jiamcs.v1i1.7","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
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.
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