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

0,5

Comments

Because the triangle A051031 is symmetric, a(n) is also the number of (2n-6)-regular graphs on 2n vertices.

Links

Table of n, a(n) for n=0..14.

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

Formula

Euler transform of A006821.

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 *)

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).

Sequence in context: A036770 A201699 A006821 * A120307 A022915 A093883

Adjacent sequences: A165623 A165624 A165625 * A165627 A165628 A165629

Keyword

nonn,hard,more

Author

Jason Kimberley, Sep 22 2009

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

Status

approved