关于递推关系αa_(i-1,j-1)+βa_(i-1,j)=a_(i,j)  

On the recurrence relation αα_(i-1,j-1)+βα_(i-1,j)=α_(i,j)

作　　者：谭明术[1] 

机构地区：[1]重庆三峡学院数学系,重庆404000

出　　处：《西南民族大学学报（自然科学版）》2004年第4期409-413,共5页Journal of Southwest Minzu University(Natural Science Edition)

基　　金：重庆市教委资助课题

摘　　要：研究了满足ααi-1,j-1+βαi-1,j=αi,j的序列{αi,j}.用发生函数法得到了n+1阶矩阵A=(αi,j)(n+1)-(n+1)的精确表达式.用数学归纳法证明(1-βx-axy)中一般项xiyi(i≥j)的系数为αjβi-j i+n-1 n-1 ij.导出了一些有关二项式系数(nk)的新的组合恒等式.Recurrence sequence {αi,j} with ααi-1,j-1+βαi-1,j=αi,j is studied. The explicit expression of n+1 order matrix A = (αi,j)(n+1)×(n+1) is obtained by using generating function. The coefficient of x1y1 in (1 - βx - axy)-n is proved to be αjβi-j i+n-1 n-1 ij by mathematical induction. In addition, some new combinatorial identities related to binomial coefficient are derived.

关 键 词：递推关系 发生函数 二项式系数 7-型矩阵 组合恒等式 

分 类 号：O157[理学—数学]