f11[x_,y_]:=a1121x+a1122y;f12[x_,y_]:=a1221x+a1222y;fx[x_,y_,z_,w_]:=a2111x+a2112y+a2131z+a2132w;fy[x_,y_,z_,w_]:=a2211x+a2212y+a2231z+a2232w;f31[x_,y_,xE_]:=a3121x+a3122y+a31ExE;f32[x_,y_,xE_]:=a3221x+a3222y+a32ExE;RSolve[{x[1]==f11[x[2],y[2]],y[1]==f12[x[2],y[2]],x[n1]==fx[x[n1-1],y[n1-1],x[n1+1],y[n1+1]],y[n1]==fy[x[n1-1],y[n1-1],x[n1+1],y[n1+1]],x[3]==f31[x[2],y[2],0],y[3]==f32[x[2],y[2],0]},{x[n1],y[n1]},n1]