一类两个指标的非常系数齐次递推式之解

A FORMULA OF SOLUTION FOR A KINDOF HOMOGENEOUS RECURRENCE OF VARIABLECOEFFICIENTS WITH TWO INDICES

给出了两个指标的非常系数齐次递堆式的显式解．该解为其系数与初始值的显函数．它为求解组合计数中的有关问题，直接提供了一个具体的计算公式．

In this paper we consider the following a kind of the homogeneous recurrence of variable coefficients with two indicesui,j=f(i,j)ui-1,j-1+g(i,j)ui-q,j-qui,0=ci,0,u0,j=c0,j(i,j=0,1, ...),ui,j=0(i < 0 or j < 0)where i, j=1, 2, ...,q≥2, f(i, j) and g (i, j) are variable numbers, ci,0 and C0,j are arbitrary constants. Itsgeneral solution is given by the following formula