{"title":"A Note on Bi-Periodic Leonardo Sequence","authors":"Paula Maria Machado Cruz Catarino, E. Spreafico","doi":"10.52737/18291163-2024.16.5-1-17","DOIUrl":"https://doi.org/10.52737/18291163-2024.16.5-1-17","url":null,"abstract":"In this work, we define a new generalization of the Leonardo sequence by the recurrence relation $GLe_n=aGLe_{n-1}+GLe_{n-2}+a$ (for even $n$) and $GLe_n=bGLe_{n-1}+GLe_{n-2}+b$ (for odd $n$) with the initial conditions $GLe_0=2a-1$ and $GLe_1=2ab-1$, where $a$ and $b$ are real nonzero numbers. Some algebraic properties of the sequence ${GLe_n}_{n geq 0}$ are studied and several identities, including the generating function and Binet's formula, are established.","PeriodicalId":505381,"journal":{"name":"Armenian Journal of Mathematics","volume":"49 8","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140978978","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}