Generating and counting triangular systems (Q1092055)

Lunnon has defined a triangular p-mino as an edge-connected configuration of p cells from the triangle plane grid with vertices of degree 6. A triangular system is a triangular p-mino without any holes. On the other hand we can say that a triangular system is a part of a triangular grid with vertices of degree 6, consisting of all edges and vertices of some closed broken line C without intersections (a circuit in the triangle grid), and all edges and vertices in the interior of C. It is obvious that any closed broken line C without intersections uniquely determines a triangular system. In this paper a method of generating triangular systems is presented.