A new generalization of Delannoy numbers
type: Item
instance of: scholarly article
title: A new generalization of Delannoy numbers
zbMATH Open document ID: 1482.11028
published in: Indian Journal of Pure \& Applied Mathematics
publication date: 2021-05-05T00:00:00Z
review text: In mathematics, a Delannoy number \(D\) describes the number of paths from the southwest corner \((0, 0)\) of a rectangular grid to the northeast corner \((m, n)\), using only single steps north, northeast, or east. The Delannoy numbers are named after French army officer and amateur mathematician Henri Delannoy. The Delannoy number \(D(m,n)\) also counts the number of global alignments of two sequences of lengths \(m\) and \(n\), the number of points in an \(m\)-dimensional integer lattice that are at most \(n\) steps from the origin and, in cellular automata, the number of cells in an \(m\)-dimensional von Neumann neighborhood of radius \(n\) while the number of cells on a surface of an \(m\)-dimensional von Neumann neighborhood of radius \(n\) is given with (sequence A266213 in the OEIS). In the paper under review, the author considers a new extension for Delannoy numbers and also derives several identities such as generating function and recurrence relations for these numbers.
Mathematics Subject Classification ID: 11B65
Mathematics Subject Classification ID: 05A15
Mathematics Subject Classification ID: 05A10
Mathematics Subject Classification ID: 42C05
zbMATH DE Number: 7344151
zbMATH Keywords: orthogonal polynomial
zbMATH Keywords: recurrence relation
zbMATH Keywords: identity
zbMATH Keywords: Delannoy numbers
author: M. Cihat Dağlı
reviewed by: Ugur Duran
describes a project that uses: SumTools
MaRDI profile type: Publication
full work available at URL: s13226-020-0492-7
OpenAlex ID: W3118713905
cites work: Why Delannoy numbers?
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cites work: A supercongruence involving Delannoy numbers and Schröder numbers
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cites work: Q4875364
cites work: A kind of orthogonal polynomials and related identities
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cites work: Supercongruences involving dual sequences
cites work: Arithmetic properties of Delannoy numbers and Schröder numbers
DOI: 10.1007/S13226-020-0492-7
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description: scientific article; zbMATH DE number 7344151