关键词: 双指标, 三项, 线性递推式, 一般解公式

Abstract: In this paper we consider the following trinomial linear recurrence with two indicis#br#u_i,j=f(i,j)u_i,j-p+ g(i,j)u_i-1,j-p + h(i,j), u_1,s=c_s(s=1,2,..,p),u_i,j=0 (i<1 or j < 1 or j ≤ q(i-1)),#br#where i,j=l, 2,...;p,q ≥ 1;f(i,j),g(i,j) and h(i,j) are variable numbers; c,(s=1, 2,.., p) are constant numbers. Its general solution is given by the formula#br#u_i,j={ F(i,j;i-1, θ₁, 1) } C_{(j-q(i-1)-pθ1)}+∑_l=1ⁱ{∑_ml=1^θ_l=1{F(i,j;i-l,θ_l+1-m_l,l)}h(l,j-q(i-l)-p(θ_l+1-m_l))}(i,j=1,2...),where θ_l=[(j-1-q(i-l)/p)(1 ≤ l ≤i).

Key words: Two indices, Trinomial, Linear recurrnce, General solution