Generating and counting triangular systems

Lunnon has defined a triangularp-mino as an edge-connected configuration ofp cells from the triangle plane grid with vertices of degree 6. A triangular system is a triangularp-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 lineC without intersections (a circuit in the triangle grid), and all edges and vertices in the interior ofC. It is obvious that any closed broken lineC without intersections uniquely determines a triangular system. In this paper a method of generating triangular systems is presented.