A165656 Number of disconnected 6-regular (sextic) graphs on n vertices.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 5, 25, 297, 8199, 377004, 22014143, 1493574756, 114880777582, 9919463450855, 955388277929620, 102101882472479938, 12050526046888229845, 1563967741064673811531, 222318116370232302781485, 34486536277291555593662301, 5817920265098158804699762770

Offset: 0

Author

Jason Kimberley, Sep 28 2009

Keywords

• nonn
• hard

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, Disconnected Graph
• Eric Weisstein's World of Mathematics, Regular Graph
• Eric Weisstein's World of Mathematics, Sextic Graph

Crossrefs

6-regular simple graphs: A006822 (connected), this sequence (disconnected), A165627 (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), this sequence (k=6), A165877 (k=7), A165878 (k=8), A185293 (k=9), A185203 (k=10), A185213 (k=11).

Formula

a = A165627 - A006822 = Euler_transformation(A006822) - A006822.

a(n) = D(n, 6) in the triangle A068933.

Extensions

Terms a(25) and beyond from Andrew Howroyd, May 20 2020