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

Author

Jason Kimberley, Sep 22 2009

Keywords

• nonn
• hard
• more

Comments

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

Links

• 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

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).

Programs

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 *)

Formula

Euler transformation of A014377.

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