A184993 Number of connected 9-regular simple graphs on 2n vertices with girth exactly 3.

0, 0, 0, 0, 0, 1, 9, 88193, 113314233813

Offset

0,7

Links

Table of n, a(n) for n=0..8.

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

Formula

a(n) = A014381(n) - A181170(n).

Example

a(0)=0 because even though the null graph (on zero vertices) is vacuously 9-regular and connected, since it is acyclic, it has infinite girth.
The a(5)=1 complete graph on 10 vertices is 9-regular; it has 45 edges and 120 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]]];
A014381 = A@014381;
A181170 = A@181170;
a[n_] := A014381[[n + 1]] - A181170[[n + 1]];
a /@ Range[0, 8] (* Jean-François Alcover, Jan 27 2020 *)

Crossrefs

Connected 9-regular simple graphs with girth at least g: A014378 (g=3), A181170 (g=4).

Connected 9-regular simple graphs with girth exactly g: this sequence (g=3).

Sequence in context: A058452 A058456 A184991 * A014381 A185293 A281360

Adjacent sequences: A184990 A184991 A184992 * A184994 A184995 A184996

Keyword

nonn,more,hard

Author

Jason Kimberley, Feb 28 2011

Status

approved