{"title":"广义类斐波那契序列的周期性","authors":"Alexander V. Evako","doi":"10.12691/AMP-5-1-2","DOIUrl":null,"url":null,"abstract":"Generalized Fibonacci-like sequences appear in finite difference approximations of the Partial Differential Equations based upon replacing partial differential equations by finite difference equations. This paper studies properties of the generalized Fibonacci-like sequence Fn+2=A+BFn+1+CFn. It is shown that this sequence is periodic with period T>2, if C= -1, |B|<2.","PeriodicalId":111854,"journal":{"name":"arXiv: Discrete Mathematics","volume":"40 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2017-02-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Periodicity of Generalized Fibonacci-like Sequences\",\"authors\":\"Alexander V. Evako\",\"doi\":\"10.12691/AMP-5-1-2\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Generalized Fibonacci-like sequences appear in finite difference approximations of the Partial Differential Equations based upon replacing partial differential equations by finite difference equations. This paper studies properties of the generalized Fibonacci-like sequence Fn+2=A+BFn+1+CFn. It is shown that this sequence is periodic with period T>2, if C= -1, |B|<2.\",\"PeriodicalId\":111854,\"journal\":{\"name\":\"arXiv: Discrete Mathematics\",\"volume\":\"40 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2017-02-10\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv: Discrete Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.12691/AMP-5-1-2\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv: Discrete Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.12691/AMP-5-1-2","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Periodicity of Generalized Fibonacci-like Sequences
Generalized Fibonacci-like sequences appear in finite difference approximations of the Partial Differential Equations based upon replacing partial differential equations by finite difference equations. This paper studies properties of the generalized Fibonacci-like sequence Fn+2=A+BFn+1+CFn. It is shown that this sequence is periodic with period T>2, if C= -1, |B|<2.
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