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A052443 Number of simple unlabeled n-node graphs of connectivity 2.

%I A052443 #37 Feb 16 2025 08:32:42
%S A052443 0,0,1,2,7,39,332,4735,113176,4629463,327695586,40525166511,
%T A052443 8850388574939,3453378695335727,2435485662537561705,
%U A052443 3137225298932374490227,7448146273273417700880931,32837456713651735794742705141,270528237651574516777595556494978,4186091025846007046878947026003803389
%N A052443 Number of simple unlabeled n-node graphs of connectivity 2.
%H A052443 Jean-François Alcover, <a href="/A052443/b052443.txt">Table of n, a(n) for n = 1..23</a>
%H A052443 Jens M. Schmidt, <a href="/A324088/a324088.html">Data files in graph6 format</a>
%H A052443 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/k-ConnectedGraph.html">k-Connected Graph.</a>
%H A052443 Gus Wiseman, <a href="/A052443/a052443.png">The a(5) = 7 graphs with vertex-connectivity 2.</a>
%F A052443 a(n) = A002218(n) - A006290(n) for n > 2. - _Andrew Howroyd_, Sep 04 2019
%t A052443 A002218 = Cases[Import["https://oeis.org/A002218/b002218.txt", "Table"], {_, _}][[All, 2]];
%t A052443 A006290 = Cases[Import["https://oeis.org/A006290/b006290.txt", "Table"], {_, _}][[All, 2]];
%t A052443 a[1] = 0; a[2] = 0; a[3] = 1;
%t A052443 a[n_] := A002218[[n]] - A006290[[n-3]];
%t A052443 Array[a, 23] (* _Jean-François Alcover_, Jan 07 2021, after _Andrew Howroyd_ *)
%Y A052443 Column k=2 of A259862.
%Y A052443 Cf. A000719, A002218, A006290, A052442, A052444, A052445.
%Y A052443 The labeled version is A327198.
%Y A052443 2-vertex-connected graphs are A013922.
%Y A052443 Cf. A322387, A327051, A327101, A327334.
%K A052443 nonn
%O A052443 1,4
%A A052443 _Eric W. Weisstein_
%E A052443 Name clarified and a(8)-a(11) by _Jens M. Schmidt_, Feb 18 2019
%E A052443 a(2)-a(3) corrected by _Andrew Howroyd_, Aug 28 2019
%E A052443 a(12)-a(20) from _Andrew Howroyd_, Sep 04 2019