A165626 Number of 5-regular graphs (quintic graphs) on 2n vertices.

1, 0, 0, 1, 3, 60, 7849, 3459386, 2585136741, 2807105258926, 4221456120848125, 8516994772686533749, 22470883220896245217626, 75883288448434648617038134, 322040154712674550886226182668

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-6)-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

Crossrefs

5-regular simple graphs: A006821 (connected), A165655 (disconnected), this sequence (not necessarily connected).

Regular graphs A005176 (any degree), A051031 (triangular array), specified degrees: A000012 (k=0), A059841 (k=1), A008483 (k=2), A005638 (k=3), A033301 (k=4), this sequence (k=5), A165627 (k=6), A165628 (k=7), A180260 (k=8).

Programs

Mathematica

A006821 = Cases[Import["https://oeis.org/A006821/b006821.txt", "Table"], {, }][[All, 2]];
(* EulerTransform is defined in A005195 *)
EulerTransform[Rest @ A006821] (* Jean-François Alcover, Dec 04 2019, updated Mar 18 2020 *)

Formula

Euler transform of A006821.

Extensions

Regular graphs cross-references edited by Jason Kimberley, Nov 07 2009

a(9) from Jason Kimberley, Nov 24 2009

a(10)-a(14) from Andrew Howroyd, Mar 10 2020