A184963 Number of connected 6-regular simple graphs on n vertices with girth exactly 3.

0, 0, 0, 0, 0, 0, 0, 1, 1, 4, 21, 266, 7848, 367860, 21609299, 1470293674, 113314233799, 9799685588930

Offset

0,10

Links

Table of n, a(n) for n=0..17.

Jason Kimberley, Index of sequences counting connected k-regular simple graphs with girth exactly g

Formula

a(n) = A006822(n) - A058276(n).

Example

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.
The a(7)=1 complete graph on 7 vertices is 6-regular; it has 21 edges and 35 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]]];
A006822 = A@006822;
A058276 = A@058276;
a[n_] := A006822[[n + 1]] - A058276[[n + 1]];
a /@ Range[0, 17] (* Jean-François Alcover, Jan 27 2020 *)

Crossrefs

Connected 6-regular simple graphs with girth at least g: A006822 (g=3), A058276 (g=4).

Connected 6-regular simple graphs with girth exactly g: this sequence (g=3), A184964 (g=4).

Sequence in context: A203218 A198004 A184960 * A185163 A184961 A006822

Adjacent sequences: A184960 A184961 A184962 * A184964 A184965 A184966

Keyword

nonn,hard,more

Author

Jason Kimberley, Feb 28 2011

Status

approved