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A184973
Number of connected 7-regular simple graphs on 2n vertices with girth exactly 3.
8
0, 0, 0, 0, 1, 5, 1547, 21609300, 733351105933
OFFSET
0,6
FORMULA
a(n) = A014377(n) - A181153(n).
EXAMPLE
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.
The a(4)=1 complete graph on 8 vertices is 7-regular; it has 28 edges and 56 triangles.
MATHEMATICA
A[s_Integer] := With[{s6 = StringPadLeft[ToString[s], 6, "0"]}, Cases[ Import["https://oeis.org/A" <> s6 <> "/b" <> s6 <> ".txt", "Table"], {_, _}][[All, 2]]];
A014377 = A@014377;
A181153 = A@181153;
a[n_] := A014377[[n + 1]] - A181153[[n + 1]];
a /@ Range[0, 8] (* Jean-François Alcover, Jan 27 2020 *)
CROSSREFS
Connected 7-regular simple graphs with girth at least g: A014377 (g=3), A181153 (g=4).
Connected 7-regular simple graphs with girth exactly g: this sequence (g=3), A184974 (g=4).
Sequence in context: A181992 A145694 A184970 * A184971 A014377 A165628
KEYWORD
nonn,more,hard
AUTHOR
Jason Kimberley, Feb 28 2011
STATUS
approved