%I #17 May 01 2014 02:37:01
%S 0,0,0,0,0,0,0,1,1,8,741,2887493
%N Number of connected 7-regular simple graphs on 2n vertices with girth exactly 4.
%H Jason Kimberley, <a href="/wiki/User:Jason_Kimberley/C_k-reg_girth_eq_g_index">Index of sequences counting connected k-regular simple graphs with girth exactly g</a>
%F a(n) = A186714(n,5) - A186715(n,5).
%e a(0)=0 because even though the null graph (on zero vertices) is vacuously 7-regular and connected, since it is acyclic, it has infinite girth.
%e The a(7)=1 graph is the complete bipartite graph K_{7,7}.
%Y Connected k-regular simple graphs with girth exactly 4: A006924 (k=3), A184944 (k=4), A184954 (k=5), A184964 (k=6), this sequence (k=7).
%Y Connected 7-regular simple graphs with girth at least g: A014377 (g=3), A181153 (g=4).
%Y Connected 7-regular simple graphs with girth exactly g: A184973 (g=3), this sequence (g=4).
%K nonn,more,hard
%O 0,10
%A _Jason Kimberley_, Feb 28 2011
|