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

0, 0, 1, 2, 7, 39, 332, 4735, 113176, 4629463, 327695586, 40525166511, 8850388574939, 3453378695335727, 2435485662537561705, 3137225298932374490227, 7448146273273417700880931, 32837456713651735794742705141, 270528237651574516777595556494978, 4186091025846007046878947026003803389

Offset: 1

Author

Eric W. Weisstein

Keywords

• nonn

Links

• Jean-François Alcover, Table of n, a(n) for n = 1..23
• Jens M. Schmidt, Data files in graph6 format
• Eric Weisstein's World of Mathematics, k-Connected Graph.
• Gus Wiseman, The a(5) = 7 graphs with vertex-connectivity 2.

Crossrefs

Column k=2 of A259862.

Cf. A000719, A002218, A006290, A052442, A052444, A052445.

The labeled version is A327198.

2-vertex-connected graphs are A013922.

Cf. A322387, A327051, A327101, A327334.

Programs

Mathematica

A002218 = Cases[Import["https://oeis.org/A002218/b002218.txt", "Table"], {, }][[All, 2]];
A006290 = Cases[Import["https://oeis.org/A006290/b006290.txt", "Table"], {, }][[All, 2]];
a[1] = 0; a[2] = 0; a[3] = 1;
a[n_] := A002218[[n]] - A006290[[n-3]];
Array[a, 23] (* Jean-François Alcover, Jan 07 2021, after Andrew Howroyd *)

Formula

a(n) = A002218(n) - A006290(n) for n > 2. - Andrew Howroyd, Sep 04 2019

Extensions

Name clarified and a(8)-a(11) by Jens M. Schmidt, Feb 18 2019

a(2)-a(3) corrected by Andrew Howroyd, Aug 28 2019

a(12)-a(20) from Andrew Howroyd, Sep 04 2019