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A165653 Number of disconnected 3-regular (cubic) graphs on 2n vertices. 12
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.

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-Fran├žois 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

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Last modified April 16 04:49 EDT 2021. Contains 343030 sequences. (Running on oeis4.)