一个有趣的三角形数表

2003年全国高考数学(理)第22题为: 设{an}是集合{2t+2s|0≤s<t,且s,t∈Z)中所有的数从小到大排列成的数列,即a1=3,a2=5,a3=6,a4=9,a5=10,a6=12,……. 将数列{an)各项按照上小下大,左小右大的原则写成如下三角形数表:

三角形数表的性质及其应用

The calculation of the number of relations on a finite set is interesting,it is related to the world famous question “the number of topology on n”.In this paper,we discussed the relation between the numbers of a curve triangle number table,it is similar to Pascal triangle,gave the number of solutions of infinite equation(*)and obtained the new combination meaning of Catalan number;similar to the second class Striling number,it is the number of equivalent class of a relation.

（a＋b＋c）^n展开式系数规律的研究

本文给出了反映三项展开式系数规律的类似'杨辉三角'的三角形数表,并给出了写出三项展开式的一般步骤,利用这个三角形数表以及文中的方法可以简便快速地写出(a+b+c)n的展开式.