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

%I A165653 #25 Feb 16 2025 08:33:11
%S A165653 0,0,0,0,1,2,9,31,147,809,5855,54477,633057,8724874,137047391,
%T A165653 2391169355,45626910415,942659626031,20937539944549,497209670658529,
%U A165653 12566853576025106,336749273734805530,9534909974420181226
%N A165653 Number of disconnected 3-regular (cubic) graphs on 2n vertices.
%H A165653 Jason Kimberley, <a href="/wiki/User:Jason_Kimberley/A068933">Disconnected regular graphs (with girth at least 3)</a>
%H A165653 Jason Kimberley, <a href="/wiki/User:Jason_Kimberley/D_k-reg_girth_ge_g_index">Index of sequences counting disconnected k-regular simple graphs with girth at least g</a>
%H A165653 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/CubicGraph.html">Cubic Graph</a>
%H A165653 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/DisconnectedGraph.html">Disconnected Graph</a>
%F A165653 a(n) = A005638(n) - A002851(n).
%F A165653 a(n) = A068933(2n, 3).
%t A165653 A[s_Integer] := With[{s6 = StringPadLeft[ToString[s], 6, "0"]}, Cases[ Import["https://oeis.org/A" <> s6 <> "/b" <> s6 <> ".txt", "Table"], {_, _}][[All, 2]]];
%t A165653 A005638 = A@005638;
%t A165653 A002851 = A@002851;
%t A165653 a[n_] := A005638[[n + 1]] - A002851[[n + 1]];
%t A165653 a /@ Range[0, 20] (* _Jean-François Alcover_, Jan 21 2020 *)
%Y A165653 3-regular simple graphs: A002851 (connected), this sequence (disconnected), A005638 (not necessarily connected).
%Y A165653 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).
%K A165653 nonn,hard
%O A165653 0,6
%A A165653 _Jason Kimberley_, Sep 28 2009