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.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
