A180260 Number of not necessarily connected 8-regular simple graphs on n vertices.

1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 6, 94, 10786, 3459386, 1470293676, 733351105935, 423187422492342, 281341168330848874, 214755319657939505396, 187549729101764460261505, 186685399408147545744203915, 210977245260028917322933165888

Offset: 0

Author

Jason Kimberley, Jan 17 2011

Keywords

• nonn
• hard

Comments

The Euler transformation currently does nothing: for n < 18, a(n) = A014378(n).

Examples

			The a(0)=1 graph is K_0 (vacuously 8-regular).
The a(9)=1 graph is K_9.
		

Links

• Eric Weisstein's World of Mathematics, Octic Graph

Crossrefs

8-regular simple graphs: A014378 (connected), A165878 (disconnected), this sequence (not necessarily connected).

Not necessarily connected regular simple graphs: A005176 (any degree), A051031 (triangular array), specified degree k: A000012 (k=0), A000012 (k=1), A008483 (k=2), A005638 (k=3), A033301 (k=4), A165626 (k=5), A165627 (k=6), A165628 (k=7), this sequence (k=8).

8-regular not necessarily connected graphs: this sequence (simple graphs), A129437 (multigraphs with loops allowed), A129426 (multigraphs with loops forbidden).

Programs

Mathematica

A014378 = Cases[Import["https://oeis.org/A014378/b014378.txt", "Table"], {, }][[All, 2]];
(* EulerTransform is defined in A005195 *)
EulerTransform[Rest @ A014378] (* Jean-François Alcover, Dec 04 2019, updated Mar 18 2020 *)

Formula

Euler transformation of A014378.

Extensions

a(17)-a(22) from Andrew Howroyd, Mar 08 2020