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%I #16 Jan 27 2020 03:55:44
%S 0,0,0,0,0,0,0,1,1,4,21,266,7848,367860,21609299,1470293674,
%T 113314233799,9799685588930
%N Number of connected 6-regular simple graphs on n 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) = A006822(n) - A058276(n).
%e a(0)=0 because even though the null graph (on zero vertices) is vacuously 6-regular and connected, since it is acyclic, it has infinite girth.
%e The a(7)=1 complete graph on 7 vertices is 6-regular; it has 21 edges and 35 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 A006822 = A@006822;
%t A058276 = A@058276;
%t a[n_] := A006822[[n + 1]] - A058276[[n + 1]];
%t a /@ Range[0, 17] (* _Jean-François Alcover_, Jan 27 2020 *)
%Y Connected 6-regular simple graphs with girth at least g: A006822 (g=3), A058276 (g=4).
%Y Connected 6-regular simple graphs with girth exactly g: this sequence (g=3), A184964 (g=4).
%K nonn,hard,more
%O 0,10
%A _Jason Kimberley_, Feb 28 2011
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