Properties of the sums of resonances found in the singularity analysis of certain classes of ordinary differential equations

In the singularity analysis of ordinary differential equations it often happens that there are various possible leading-order behaviours. It is observed that the sums of the resonances in certain instances are the same. We illustrate this with certain examples from differential sequences and higher-order equations of Bureau symbol P2. For the Riccati Differential Sequence we prove two generic properties dealing with the occurrence of the coefficients of the leading-order term and the variation of the sum of the resonances. An explanation of observed discrepancies in the cases of fourth- and fifth-order equations of Bureau symbol P2 is presented.