A165628 Number of 7-regular graphs (septic graphs) on 2n vertices.

1, 0, 0, 0, 1, 5, 1547, 21609301, 733351105935, 42700033549946255, 4073194598236125134140, 613969628444792223023625238, 141515621596238755267618266465449

Offset

0,6

Comments

Because the triangle A051031 is symmetric, a(n) is also the number of (2n-8)-regular graphs on 2n vertices.

Links

Table of n, a(n) for n=0..12.

Jason Kimberley, Index of sequences counting not necessarily connected k-regular simple graphs with girth at least g

M. Meringer, Tables of Regular Graphs

M. Meringer, Fast generation of regular graphs and construction of cages, J. Graph Theory 30 (2) (1999) 137-146.

N. J. A. Sloane, Transforms

Eric Weisstein's World of Mathematics, Septic Graph

Formula

Euler transformation of A014377.

Mathematica

A014377 = Cases[Import["https://oeis.org/A014377/b014377.txt", "Table"], {_, _}][[All, 2]];
(* EulerTransform is defined in A005195 *)
EulerTransform[Rest @ A014377] (* Jean-François Alcover, Dec 04 2019, updated Mar 18 2020 *)

Crossrefs

7-regular simple graphs: A014377 (connected), A165877 (disconnected), this sequence (not necessarily connected).

Regular graphs A005176 (any degree), A051031 (triangular array), chosen degrees: A000012 (k=0), A059841 (k=1), A008483 (k=2), A005638 (k=3), A033301 (k=4), A165626 (k=5), A165627 (k=6), this sequence (k=7), A180260 (k=8).

Sequence in context: A184973 A184971 A014377 * A119747 A177906 A127106

Adjacent sequences: A165625 A165626 A165627 * A165629 A165630 A165631

Keyword

nonn,hard,more

Author

Jason Kimberley, Sep 22 2009

Extensions

Cross-references edited by Jason Kimberley, Nov 07 2009 and Oct 17 2011

a(9)-a(11) from Andrew Howroyd, Mar 09 2020

a(12) from Andrew Howroyd, May 19 2020

Status

approved