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1)linear additive model,ÏßÐԵݼÓģʽ

2)linear recurrence formula,ÏßÐÔµÝÍÆʽ

3)linear recurrence,ÏßÐÔµÝÍÆʽ

4)Fractional linear recurrence formula,·ÖʽÏßÐÔµÝÍÆʽ

5)linear iteration relations,ÏßÐÔµÝÍƹØϵʽ

6)bilinear recurrent relation,Ë«ÏßÐÔµÝÍÆʽ

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By using Frobenius matrix, this paper presents the common solution in another form to linear recurrence formula with constant coefficients.

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In this paper we consider the following class of linear recurrence with variable coefficients with two indicesª§ª§u i,j =f(i,j)u i-1,j-1 +g(i,j)u i-q,j-q +h(i,j), u i,0 =c i,0 ,u 0,j =c 0,j (i,j=0,1,¡­),u i,j =0(i<0 or j<0),ª§ª§where ª§i,j=1,2,¡­,q¡Ý2,f(i,j),g(i,j)ª§ and ª§h(i,j) (i,j¡Ý1)ª§ are variable numbers,ª§c i,0 ª§ and ª§c 0,j (i,j=0,1,¡­)ª§ are vrbitrary constants.

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It is very difficult to get a clear formula solution of general linear recurrence,even for the case of homogeneous recurrence of constantcoefficients with one indicds.

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