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

0,10

Links

Table of n, a(n) for n=0..16.

Maciej Demianowicz, Progress in the study of the (non)existence of genuinely unextendible product bases, Quantum Info. Proc. 25 (2026), 67. See also arXiv:2509.26135 [quant-ph], 2025. See references.

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.

N. J. A. Sloane, Transforms.

Eric Weisstein's World of Mathematics, Septic Graph

Formula

a(n) = A165628(n) - A014377(n), i.e., Euler_transformation(A014377) - A014377.

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

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).

Sequence in context: A119747 A177906 A127106 * A366830 A123658 A262628

Adjacent sequences: A165874 A165875 A165876 * A165878 A165879 A165880

Keyword

nonn,hard,more

Author

Jason Kimberley, Sep 28 2009

Extensions

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

Status

approved