具有限制条件的Motzkin路的计数问题

Enumeration on restricted Motzkin paths

在原有Motzkin路的基础上,构造具有限制条件的Motzkin路:从原点出发,在直线y=m上方连续步长的最大值小于事先给定的正整数t,最终回到任意直线y=l的路,其中l是小于m∈N+的非负整数.并推导出在此限制条件下从(0,0)到(n,l)的Motzkin路的计数公式.

Based on the original Motzkin paths, author discussed the restricted Motakin paths which start from the origin and finally return to the line y=l such that the maximal number of continuous steps above the line y= m is less that a given positive integer, where l is a nonnegative integer which is less than m ∈ N^＋. At last, author derived it＇s enumerative formulas.