{"title":"用交替方法求四数列的Binet型公式","authors":"Gautam S. Hathiwala, D. V. Shah","doi":"10.15415/mjis.2017.61004","DOIUrl":null,"url":null,"abstract":"The sequence {Tn} of Tetranacci numbers is defined by recurrence relation Tn= Tn-1 + Tn-2 + Tn-3 + Tn-4; n≥4 with initial condition T0=T1=T2=0 and T3=1. In this Paper, we obtain the explicit formulla-Binet-type formula for Tn by two different methods. We use the concept of Eigen decomposition as well as of generating functions to obtain the result.","PeriodicalId":166946,"journal":{"name":"Mathematical Journal of Interdisciplinary Sciences","volume":"102 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2019-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"18","resultStr":"{\"title\":\"Binet – Type Formula For The Sequence of Tetranacci Numbers by Alternate Methods\",\"authors\":\"Gautam S. Hathiwala, D. V. Shah\",\"doi\":\"10.15415/mjis.2017.61004\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The sequence {Tn} of Tetranacci numbers is defined by recurrence relation Tn= Tn-1 + Tn-2 + Tn-3 + Tn-4; n≥4 with initial condition T0=T1=T2=0 and T3=1. In this Paper, we obtain the explicit formulla-Binet-type formula for Tn by two different methods. We use the concept of Eigen decomposition as well as of generating functions to obtain the result.\",\"PeriodicalId\":166946,\"journal\":{\"name\":\"Mathematical Journal of Interdisciplinary Sciences\",\"volume\":\"102 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2019-05-23\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"18\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematical Journal of Interdisciplinary Sciences\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.15415/mjis.2017.61004\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematical Journal of Interdisciplinary Sciences","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.15415/mjis.2017.61004","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Binet – Type Formula For The Sequence of Tetranacci Numbers by Alternate Methods
The sequence {Tn} of Tetranacci numbers is defined by recurrence relation Tn= Tn-1 + Tn-2 + Tn-3 + Tn-4; n≥4 with initial condition T0=T1=T2=0 and T3=1. In this Paper, we obtain the explicit formulla-Binet-type formula for Tn by two different methods. We use the concept of Eigen decomposition as well as of generating functions to obtain the result.
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