A165653 - OEIS

A165653

Number of disconnected 3-regular (cubic) graphs on 2n vertices.

0, 0, 0, 0, 1, 2, 9, 31, 147, 809, 5855, 54477, 633057, 8724874, 137047391, 2391169355, 45626910415, 942659626031, 20937539944549, 497209670658529, 12566853576025106, 336749273734805530, 9534909974420181226

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,6

LINKS

Table of n, a(n) for n=0..22.

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.

Eric Weisstein's World of Mathematics, Cubic Graph.

Eric Weisstein's World of Mathematics, Disconnected Graph.

FORMULA

a(n) = A005638(n) - A002851(n).

a(n) = A068933(2n, 3).

MATHEMATICA

A[s_Integer] := With[{s6 = StringPadLeft[ToString[s], 6, "0"]}, Cases[ Import["https://oeis.org/A" <> s6 <> "/b" <> s6 <> ".txt", "Table"], {_, _}][[All, 2]]];

A005638 = A@005638;

A002851 = A@002851;

a[n_] := A005638[[n + 1]] - A002851[[n + 1]];

a /@ Range[0, 20] (* Jean-François Alcover, Jan 21 2020 *)

CROSSREFS

3-regular simple graphs: A002851 (connected), this sequence (disconnected), A005638 (not necessarily connected).

Disconnected regular simple graphs: A068932 (any degree), A068933 (triangular array), specified degree k: A165652 (k=2), this sequence (k=3), A033483 (k=4), A165655 (k=5), A165656 (k=6), A165877 (k=7), A165878 (k=8), A185293 (k=9), A185203 (k=10), A185213 (k=11).

Sequence in context: A150910 A150911 A150912 * A182265 A212873 A109770

Adjacent sequences: A165650 A165651 A165652 * A165654 A165655 A165656

KEYWORD

nonn,hard

AUTHOR

Jason Kimberley, Sep 28 2009

STATUS

approved