cp's OEIS Frontend

Label vertices of F_{n,4} with v1, ..., v_n, a, b, c, d with be adjacent to a and c and d adjacent to c. An edge cover is a subset of the edges so that each vertex is the endpoint of at least one edge. Each of the n vertices has 15 ways to connect to vertices a, b, c, d. Once we connect all v_i's, we then have 8 options for the edges ab, bc, and cd to exist or not, giving 8*15^n options. But not all of these will be an edge cover. For example, if all v_i's connect to only b and c, we have to add edges ab and cd in the second step. So, 12*7^n options are removed. However, we removed too many options here. This line of reasoning continues, following the Inclusion-Exclusion Principle, to obtain the remaining pieces of the formula for a(n).