摘要
利用Riordan矩阵的A序列和Z序列得到了水平步、上步和下步加权的Motzkin路和Riordan路的矩阵表达式,并利用拉格朗日反演公式计算得出其一般元.最后证明了水平步、上步和下步加权分别为α,β,γ的Motzkin数的递推关系式.
We consider the Motzkin paths and Riordan paths that use the steps Level,Up,and Down with assigned weightedα;β;γ.The counting matrix of the weighted Motzkin paths and Riordan paths are obtained by using A-sequences and Z-sequences of the Riordan array.The entries of the matrix are computed by means of the Lagrange inversion formula.Finally,we give a algebraic proof of a three-term recursion identities for a weighted Motzkin sequence.
作者
辛华
杨胜良
Xin Hua;Yang Shengliang(School of Science,Lanzhou University of Technology,Lanzhou 710069,China)
出处
《纯粹数学与应用数学》
2018年第3期301-308,共8页
Pure and Applied Mathematics
基金
国家自然科学基金(11561044)