A Context-Free Grammar Associated with Fibonacci and Lucas Sequences
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...
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2023-01-01
|
| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2023/6497710 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832547340188123136 |
|---|---|
| author | Harold Ruilong Yang |
| author_facet | Harold Ruilong Yang |
| author_sort | Harold Ruilong Yang |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-1b96d892ddfc40d481ad82b62b08a8f8 |
| institution | Kabale University |
| issn | 2314-4785 |
| language | English |
| publishDate | 2023-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-1b96d892ddfc40d481ad82b62b08a8f82025-02-03T06:45:15ZengWileyJournal of Mathematics2314-47852023-01-01202310.1155/2023/6497710A Context-Free Grammar Associated with Fibonacci and Lucas SequencesHarold Ruilong Yang0School of ScienceWe 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.http://dx.doi.org/10.1155/2023/6497710 |
| spellingShingle | Harold Ruilong Yang A Context-Free Grammar Associated with Fibonacci and Lucas Sequences Journal of Mathematics |
| title | A Context-Free Grammar Associated with Fibonacci and Lucas Sequences |
| title_full | A Context-Free Grammar Associated with Fibonacci and Lucas Sequences |
| title_fullStr | A Context-Free Grammar Associated with Fibonacci and Lucas Sequences |
| title_full_unstemmed | A Context-Free Grammar Associated with Fibonacci and Lucas Sequences |
| title_short | A Context-Free Grammar Associated with Fibonacci and Lucas Sequences |
| title_sort | context free grammar associated with fibonacci and lucas sequences |
| url | http://dx.doi.org/10.1155/2023/6497710 |
| work_keys_str_mv | AT haroldruilongyang acontextfreegrammarassociatedwithfibonacciandlucassequences AT haroldruilongyang contextfreegrammarassociatedwithfibonacciandlucassequences |