A combinatorial proof of a recursive relation of the Motzkin sequence by lattice paths (Q2785021)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: A combinatorial proof of a recursive relation of the Motzkin sequence by lattice paths |
scientific article; zbMATH DE number 1733233
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A combinatorial proof of a recursive relation of the Motzkin sequence by lattice paths |
scientific article; zbMATH DE number 1733233 |
Statements
2 December 2002
0 references
Motzkin number
0 references
recursion
0 references
A combinatorial proof of a recursive relation of the Motzkin sequence by lattice paths (English)
0 references
Let \(m_n\) be the \(n\)th Motzkin number. The first few Motzkin numbers are \(1,1,2,4,9,21,51,\dots\) In this paper the author gives a combinatorial proof of the recursion of the Motzkin sequence showing that \((n+ 4)m_{n+2}= (2n+5)m_{n+1}+ 3(n+1)m_n\) \((n\geq 0)\), and also that \(\lim_{n\to\infty} m_{n+1}/m_n= 3\).
0 references
