General form of some rational recursive sequences

In this note, we study the general form of some rational recursive sequences. By some modification of the methods and ideas, as well as the transformation from the paper [K. S. Berenhaut, J. D. Foley and S. Stević, The global attractivity of the rational difference equation yn=yn−k+yn−m1+yn−kyn−m, Appl. Math. Lett. 20 (2007), 54–58], we give a new proof for the conjectures posed therein.