{"title":"从四阶差分方程到四元数代数的迷人数列","authors":"A. Patra","doi":"10.7151/dmgaa.1369","DOIUrl":null,"url":null,"abstract":"Abstract The balancing and Lucas-balancing numbers are solutions of second order recurrence relations. A linear combination of these numbers can also be obtained as solutions of a fourth order recurrence relation. This recurrence relation can be extended to generalized quaternion algebras. Also, the fourth order recurrence relation has application in coding theory.","PeriodicalId":36816,"journal":{"name":"Discussiones Mathematicae - General Algebra and Applications","volume":"41 1","pages":"229 - 237"},"PeriodicalIF":0.0000,"publicationDate":"2021-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Fascinating Number Sequences from Fourth Order Difference Equation Via Quaternion Algebras\",\"authors\":\"A. Patra\",\"doi\":\"10.7151/dmgaa.1369\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract The balancing and Lucas-balancing numbers are solutions of second order recurrence relations. A linear combination of these numbers can also be obtained as solutions of a fourth order recurrence relation. This recurrence relation can be extended to generalized quaternion algebras. Also, the fourth order recurrence relation has application in coding theory.\",\"PeriodicalId\":36816,\"journal\":{\"name\":\"Discussiones Mathematicae - General Algebra and Applications\",\"volume\":\"41 1\",\"pages\":\"229 - 237\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2021-09-06\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Discussiones Mathematicae - General Algebra and Applications\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.7151/dmgaa.1369\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Discussiones Mathematicae - General Algebra and Applications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.7151/dmgaa.1369","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"Mathematics","Score":null,"Total":0}
Fascinating Number Sequences from Fourth Order Difference Equation Via Quaternion Algebras
Abstract The balancing and Lucas-balancing numbers are solutions of second order recurrence relations. A linear combination of these numbers can also be obtained as solutions of a fourth order recurrence relation. This recurrence relation can be extended to generalized quaternion algebras. Also, the fourth order recurrence relation has application in coding theory.
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