A165877 Number of disconnected 7-regular (septic) graphs on 2n vertices.

0, 0, 0, 0, 0, 0, 0, 0, 1, 5, 1562, 21617036, 733460349818, 42703733735064572, 4073409466378991404239, 613990076321940092226829047, 141518698937232822678583027258225

Offset: 0

Author

Jason Kimberley, Sep 28 2009

Keywords

• nonn
• hard
• more

Links

• N. J. A. Sloane, Transforms
• Jason Kimberley, Disconnected regular graphs (with girth at least 3)
• Jason Kimberley, Index of sequences counting disconnected k-regular simple graphs with girth at least g
• Eric Weisstein's World of Mathematics, Septic Graph

Crossrefs

7-regular simple graphs: A014377 (connected), this sequence(disconnected), A165628 (not necessarily connected).

Disconnected regular simple graphs: A068932 (any degree), A068933 (triangular array), specified degree k: A165652 (k=2), A165653 (k=3), A033483 (k=4), A165655 (k=5), A165656 (k=6), this sequence (k=7), A165878 (k=8), A185293 (k=9), A185203 (k=10), A185213 (k=11).

Formula

a = A165628 - A014377 = Euler_transformation(A014377) - A014377.

a(n)=D(2n, 7) in the triangle A068933.

Extensions

a(13)-a(16) from Andrew Howroyd, May 20 2020