| On the $(m,r,s)$-Halves of a Riordan Array and Applications |
| Received:May 10, 2022 Revised:August 22, 2022 |
| Key Words:
Riordan array central coefficients Pascal matrix Delannoy matrix Fibonacci numbers Pell numbers Jacobsthal numbers
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| Fund Project:Supported by the National Natural Science Foundation of China (Grant Nos.12101280;11861045) and the Science Foundation for Youths of Gansu Province (Grant No.20JR10RA187). |
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| Abstract: |
| Given a Riordan array, its vertical half and horizontal half are studied separately before. In the present paper, we introduce the $(m,r,s)$-halves of a Riordan array. This allows us to discuss the vertical half and horizontal half in a uniform context. As applications, we find several new identities involving Fibonacci, Pell and Jacobsthal sequences by applying the $(m,r,s)$-halves of Pascal and Delannoy matrices. |
| Citation: |
| DOI:10.3770/j.issn:2095-2651.2023.03.001 |
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