A165655 Number of disconnected 5-regular (quintic) graphs on 2n vertices.

0, 0, 0, 0, 0, 0, 1, 3, 66, 8029, 3484760, 2595985770, 2815099031417, 4230059694039460, 8529853839173455678, 22496718465713456081402, 75951258300080722467845995, 322269241532759484921710401976

Offset

0,8

Links

Table of n, a(n) for n=0..17.

Maciej Demianowicz, Progress in the study of the (non)existence of genuinely unextendible product bases, Quantum Info. Proc. 25 (2026), 67.

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, Disconnected Graph.

Eric Weisstein's World of Mathematics, Quintic Graph.

Formula

a = A165626 - A006821 = Euler_transformation(A006821) - A006821.

a(n)=A068933(2n,5).

Crossrefs

5-regular simple graphs: A006821 (connected), this sequence (disconnected), A165626 (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), this sequence (k=5), A165656 (k=6), A165877 (k=7), A165878 (k=8), A185293 (k=9), A185203 (k=10), A185213 (k=11).

Sequence in context: A384025 A157554 A185053 * A157576 A339599 A105443

Adjacent sequences: A165652 A165653 A165654 * A165656 A165657 A165658

Keyword

nonn,hard,more

Author

Jason Kimberley, Sep 28 2009

Extensions

Terms a(13)-a(17), due to the extension of A006821 by Andrew Howroyd, from Jason Kimberley, Mar 12 2020

Status

approved