On families of cubic split Thue equations parametrised by linear recurrence sequences

We show that the split family of cubic Thue Equations \[ X(X-A_nY)(X-B_nY)-Y^3 = \pm 1, \] with linear recurrence sequences A_n, B_nsatisfying a dominant root condition each, has but the trivial solutions when the parameter nis smaller than an effectively computable...