{"title":"Generalized Fibonacci–Leonardo numbers","authors":"Urszula Bednarz, Małgorzata Wołowiec-Musiał","doi":"10.1080/10236198.2023.2265509","DOIUrl":null,"url":null,"abstract":"AbstractIn this paper, by means of independent sets in a graph with multiplicity assigned to each set, we introduce generalized Fibonacci–Leonardo numbers, which are the common generalization of the classical Fibonacci and Leonardo numbers. We give the Binet formula, the generating function, and we prove some identities for generalized Fibonacci–Leonardo numbers. We also define matrix generators for the introduced numbers.Keywords: Fibonacci numbersLeonardo numbersindependent setsmatrix generatorAMS CLASSIFICATIONS: 11B3711B3911C20 AcknowledgmentsThe authors wish to thank the referee for all suggestions which improved this paper.Disclosure statementNo potential conflict of interest was reported by the author(s).","PeriodicalId":15616,"journal":{"name":"Journal of Difference Equations and Applications","volume":"8 1","pages":"0"},"PeriodicalIF":1.0000,"publicationDate":"2023-10-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Difference Equations and Applications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1080/10236198.2023.2265509","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
AbstractIn this paper, by means of independent sets in a graph with multiplicity assigned to each set, we introduce generalized Fibonacci–Leonardo numbers, which are the common generalization of the classical Fibonacci and Leonardo numbers. We give the Binet formula, the generating function, and we prove some identities for generalized Fibonacci–Leonardo numbers. We also define matrix generators for the introduced numbers.Keywords: Fibonacci numbersLeonardo numbersindependent setsmatrix generatorAMS CLASSIFICATIONS: 11B3711B3911C20 AcknowledgmentsThe authors wish to thank the referee for all suggestions which improved this paper.Disclosure statementNo potential conflict of interest was reported by the author(s).
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Journal of Difference Equations and Applications presents state-of-the-art papers on difference equations and discrete dynamical systems and the academic, pure and applied problems in which they arise. The Journal is composed of original research, expository and review articles, and papers that present novel concepts in application and techniques.
The scope of the Journal includes all areas in mathematics that contain significant theory or applications in difference equations or discrete dynamical systems.
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