Bases of recurrent sequences

This paper provides an overview of the results (with varying degrees of detail) in three different directions.
The main Central direction refers to recurrent sequences, primarily to their base (in a different sense) sets.
Another direction is related to new combinatorial objects $(v,k_1,k_2)$-configurations encountered on the way of weakening the determinants of well-known combinatorial objects $(v,k,\lambda)$-configuration.
The third direction deals with invariant differentials of higher orders from several smooth functions of one real variable.
In each of these themes the issues associated with combinatorial configurations in the form of finite planes, and the results obtained through the same type of views, points of the corresponding configurations of points in multidimensional locally Euclidean spaces. In the case of invariant differentials of these representations arise naturally, and in the case of recurrent sequences and $(v,k_1,k_2)$-configurations are introduced by analogy, but in an artificial way.
Bibliography: 39 titles.