A Context-Free Grammar Associated with Fibonacci and Lucas Sequences

Harold Ruilong Yang and Chang Phang

Journal of Mathematics, 2023, vol. 2023, 1-9

Abstract: 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.

Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:6497710

DOI: 10.1155/2023/6497710

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