{"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":1,"journal":{"name":"Accounts of Chemical Research","volume":null,"pages":null},"PeriodicalIF":16.4000,"publicationDate":"2023-10-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Accounts of Chemical Research","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1080/10236198.2023.2265509","RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","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).
期刊介绍：
Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance.
Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.
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