

A184983


Number of connected 8regular simple graphs on n vertices with girth exactly 3.


9



0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 6, 94, 10786, 3459386, 1470293676, 733351105934
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OFFSET

0,12


LINKS

Table of n, a(n) for n=0..16.
Jason Kimberley, Index of sequences counting connected kregular simple graphs with girth exactly g


FORMULA

a(n) = A014378(n)  A181154(n).


EXAMPLE

a(0)=0 because even though the null graph (on zero vertices) is vacuously 8regular and connected, since it is acyclic, it has infinite girth.
The a(9)=1 complete graph on 9 vertices is 8regular; it has 36 edges and 84 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]]];
A014378 = A@014378;
A181154 = A@181154;
a[n_] := A014378[[n + 1]]  A181154[[n + 1]];
a /@ Range[0, 16] (* JeanFrançois Alcover, Jan 27 2020 *)


CROSSREFS

Connected 8regular simple graphs with girth at least g: A014378 (g=3), A181154 (g=4).
Connected 8regular simple graphs with girth exactly g: this sequence (g=3).
Sequence in context: A321073 A198257 A296820 * A184980 A184981 A014378
Adjacent sequences: A184980 A184981 A184982 * A184984 A184985 A184986


KEYWORD

nonn,hard,more


AUTHOR

Jason Kimberley, Feb 28 2011


STATUS

approved



