一类两个指标的非常系数齐次递推式之解

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 余长安 Yu Chang’an 1 2 first-author 武汉大学数学科学学院,武汉 武汉大学数学科学学院,武汉 College of Mathematical Sciences, Wuhan University College of Mathematical Sciences, Wuhan University ,430072 ,430072 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 两个指标 非常系数 齐次递推式 显式解 two indices variable coefficients homogeneous recurrence explict solution O241 高等学校博士点基金;国家自然科学基金(61672102) 1998-05-01 2021-04-01 5