A184963 - OEIS

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

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

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