Riordan 矩阵的$(m,r,s)$-Halves

On the $(m,r,s)$-Halves of a Riordan Array and Applications

中文关键词:  Riordan矩阵  中心系数 Pascal矩阵  Delannoy矩阵  Fibonacci数  Pell数  Jacobsthal数

英文关键词:Riordan array  central coefficients  Pascal matrix  Delannoy matrix  Fibonacci numbers  Pell numbers  Jacobsthal numbers

中文摘要:

      Riordan矩阵的垂直一半和水平一半已经被许多学者分别研究过.本文给出了Riordan矩阵的$(m,r,s)$-halves的定义.利用此定义能够统一的讨论Riordan矩阵的垂直一半和水平一半.作为应用,通过对Pascal和Delannoy矩阵的$(m,r,s)$-halves的研究,可以得到了一些与Fibonacci, Pell和Jacobsthal序列相关的等式.

英文摘要:

      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.