Solving non-homogeneous nested recursions using trees (Q2441387)

In this well written paper, it is shown how certain nested non-homogeneous versions of \(k\)-term nested recursions including a constant term are connected to counting \(n\) leaves in certain infinte trees corresponding to these recursions using a tree grafting method that inserts copies of a finite tree in it. Also if the initial conditions are varied the same terchnique leads to a solution.