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%I #15 Jan 27 2020 03:55:11
%S 0,0,0,0,0,0,0,0,0,1,1,6,94,10786,3459386,1470293676,733351105934
%N Number of connected 8-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) = A014378(n) - A181154(n).
%e a(0)=0 because even though the null graph (on zero vertices) is vacuously 8-regular and connected, since it is acyclic, it has infinite girth.
%e The a(9)=1 complete graph on 9 vertices is 8-regular; it has 36 edges and 84 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 A014378 = A@014378;
%t A181154 = A@181154;
%t a[n_] := A014378[[n + 1]] - A181154[[n + 1]];
%t a /@ Range[0, 16] (* _Jean-François Alcover_, Jan 27 2020 *)
%Y Connected 8-regular simple graphs with girth at least g: A014378 (g=3), A181154 (g=4).
%Y Connected 8-regular simple graphs with girth exactly g: this sequence (g=3).
%K nonn,hard,more
%O 0,12
%A _Jason Kimberley_, Feb 28 2011
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