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A184993 Number of connected 9-regular simple graphs on 2n vertices with girth exactly 3.

%I A184993 #14 Jan 27 2020 07:36:57
%S A184993 0,0,0,0,0,1,9,88193,113314233813
%N A184993 Number of connected 9-regular simple graphs on 2n vertices with girth exactly 3.
%H A184993 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 A184993 a(n) = A014381(n) - A181170(n).
%e A184993 a(0)=0 because even though the null graph (on zero vertices) is vacuously 9-regular and connected, since it is acyclic, it has infinite girth.
%e A184993 The a(5)=1 complete graph on 10 vertices is 9-regular; it has 45 edges and 120 triangles.
%t A184993 A[s_Integer] := With[{s6 = StringPadLeft[ToString[s], 6, "0"]}, Cases[ Import["https://oeis.org/A" <> s6 <> "/b" <> s6 <> ".txt", "Table"], {_, _}][[All, 2]]];
%t A184993 A014381 = A@014381;
%t A184993 A181170 = A@181170;
%t A184993 a[n_] := A014381[[n + 1]] - A181170[[n + 1]];
%t A184993 a /@ Range[0, 8] (* _Jean-François Alcover_, Jan 27 2020 *)
%Y A184993 Connected 9-regular simple graphs with girth at least g: A014378 (g=3), A181170 (g=4).
%Y A184993 Connected 9-regular simple graphs with girth exactly g: this sequence (g=3).
%K A184993 nonn,more,hard
%O A184993 0,7
%A A184993 _Jason Kimberley_, Feb 28 2011