A Context-Free Grammar Associated with Fibonacci and Lucas Sequences

被引：0
|
作者：
Yang, Harold Ruilong [1 ]
机构：
[1] Tianjin Univ Technol & Educ, Sch Sci, Tianjin 300222, Peoples R China
来源：
JOURNAL OF MATHEMATICS | 2023年 / 2023卷
基金：
中国国家自然科学基金; 美国国家科学基金会;
关键词：
D O I：
10.1155/2023/6497710
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We introduce a context-free grammar G = {s -> s + d, d -> s} to generate Fibonacci and Lucas sequences. By applying the grammar G, we give a grammatical proof of the Binet formula. Besides, we use the grammar G to provide a unified approach to prove several binomial convolutions about Fibonacci and Lucas numbers, which were given by Hoggatt, Carlitz, and Church. Meanwhile, we also obtain some new binomial convolutions.
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页数：9
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