Abstract
Graham Higman was the first who studied the transitive actions of the extended modular group PGL(2, Z) over PL(F-q) = F-q boolean OR(I infinity) graphically and named it as coset diagram. In these sorts of graphs, a closed path of edges and triangles is known as a circuit. Coset diagrams evolve through the joining of these circuits. In a coset diagram, a circuit is termed as a length-l circuit if its one vertex is fixed by (x(1)x(2))(pi 1)(x(1)x(2)(-1))(pi 2)(x(1)x(2)) (pi 3), . . ., (x(1)x(2)(-1))(pi 1) is an element of PSL(2 , Z), and it is denoted by ( pi(1),pi(2),pi(3,), . . . ,pi(1)) .In this study, we shall formulate combinatorial sequences and find the number of distinct equivalence classes of a length-6 circuit (pi(1),pi(2),pi(3),pi(4),pi(5),pi(6)) for a fixed number of triangle Delta of class Pi.