%I #13 Jan 27 2020 03:55:01

%S 0,0,0,0,1,5,1547,21609300,733351105933

%N Number of connected 7-regular simple graphs on 2n vertices with girth exactly 3.

%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) = A014377(n) - A181153(n).

%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(4)=1 complete graph on 8 vertices is 7-regular; it has 28 edges and 56 triangles.

%t A[s_Integer] := With[{s6 = StringPadLeft[ToString[s], 6, "0"]}, Cases[ Import["https://oeis.org/A" <> s6 <> "/b" <> s6 <> ".txt", "Table"], {_, _}][[All, 2]]];

%t A014377 = A@014377;

%t A181153 = A@181153;

%t a[n_] := A014377[[n + 1]] - A181153[[n + 1]];

%t a /@ Range[0, 8] (* _Jean-François Alcover_, Jan 27 2020 *)

%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: this sequence (g=3), A184974 (g=4).

%K nonn,more,hard

%O 0,6

%A _Jason Kimberley_, Feb 28 2011