------------------------------

       Let's take z0=3, and try to factorize the Dimer C-finite sequences



                                    n is, 4



[[[3*RootOf(_Z^4-3*_Z^2+1), 1], [-3*RootOf(_Z^4-3*_Z^2+1)*(RootOf(_Z^4-3*_Z^2+1
)^2-3), 1]]]


                                    n is, 6



[[[3*RootOf(_Z^6-5*_Z^4+6*_Z^2-1), 1], [9*RootOf(_Z^6-5*_Z^4+6*_Z^2-1)*(RootOf(
_Z^6-5*_Z^4+6*_Z^2-1)^4-5*RootOf(_Z^6-5*_Z^4+6*_Z^2-1)^2+6), -9*RootOf(_Z^6-5*
_Z^4+6*_Z^2-1)^2+47, 9*RootOf(_Z^6-5*_Z^4+6*_Z^2-1)*(RootOf(_Z^6-5*_Z^4+6*_Z^2-\
1)^4-5*RootOf(_Z^6-5*_Z^4+6*_Z^2-1)^2+6), -1]]]


                                    n is, 8



[[[3*RootOf(_Z^2-1), 1], [27*RootOf(_Z^2-1), 841, 1593*RootOf(_Z^2-1), -951, -\
1593*RootOf(_Z^2-1), 841, -27*RootOf(_Z^2-1), -1]]]