Nur Şeyma Yilmaz, A. Włoch, Engin Özkan, Dominik Strzałka
{"title":"On Doubled and Quadrupled Fibonacci Type Sequences","authors":"Nur Şeyma Yilmaz, A. Włoch, Engin Özkan, Dominik Strzałka","doi":"10.2478/amsil-2023-0020","DOIUrl":null,"url":null,"abstract":"Abstract In this paper we study a family of doubled and quadrupled Fibonacci type sequences obtained by distance generalization of Fibonacci sequence. In particular we obtain doubled Fibonacci sequence, doubled and quadrupled Padovan sequence and quadrupled Narayana’s sequence. We give a binomial direct formula for these sequences using graph methods, and also we derive a number of identities. Moreover, we study matrix generators of these sequences and determine connections with the Pascal’s triangle.","PeriodicalId":502615,"journal":{"name":"Annales Mathematicae Silesianae","volume":"175 ","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2023-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annales Mathematicae Silesianae","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.2478/amsil-2023-0020","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
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Abstract
Abstract In this paper we study a family of doubled and quadrupled Fibonacci type sequences obtained by distance generalization of Fibonacci sequence. In particular we obtain doubled Fibonacci sequence, doubled and quadrupled Padovan sequence and quadrupled Narayana’s sequence. We give a binomial direct formula for these sequences using graph methods, and also we derive a number of identities. Moreover, we study matrix generators of these sequences and determine connections with the Pascal’s triangle.
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