A184973 - OEIS

A184973

Number of connected 7-regular simple graphs on 2n vertices with girth exactly 3.

0, 0, 0, 0, 1, 5, 1547, 21609300, 733351105933

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,6

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) = 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

Adjacent sequences: A184970 A184971 A184972 * A184974 A184975 A184976

KEYWORD

nonn,more,hard

AUTHOR

Jason Kimberley, Feb 28 2011

STATUS

approved