A241767 Number of simple connected graphs with n nodes and exactly 1 articulation point (cutpoints).

0, 0, 1, 2, 7, 33, 244, 2792, 52448, 1690206, 96288815, 9873721048, 1841360945834, 629414405238720, 397024508142598996, 464923623652122023478, 1016016289424631486429082, 4162473006943138723685574978, 32096861904411547975392065322659

Offset: 1

Author

Travis Hoppe and Anna Petrone, Apr 28 2014

Keywords

• nonn

Comments

Terms may be computed from A004115. See formula. There is an obvious bijection between a connected graph with 1 articulation point and a multiset of at least two rooted nonseparable graphs joined at the root node. - Andrew Howroyd, Nov 24 2020

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..26
• Travis Hoppe and Anna Petrone, Encyclopedia of Finite Graphs
• T. Hoppe and A. Petrone, Integer sequence discovery from small graphs, arXiv preprint arXiv:1408.3644 [math.CO], 2014.
• Eric Weisstein's World of Mathematics, Articulation Vertex

Crossrefs

Column k=1 of A325111.

Cf. other simple connected graph sequences with k articulation points A002218, A241767, A241768, A241769, A241770, A241771.

Cf. A004115 (rooted and without articulation points).

Formula

G.f.: x/(Product_{k>=1} (1 - x^k)^A004115(k+1)) - x - Sum_{k>=1} A004115(k)*x^k. - Andrew Howroyd, Nov 24 2020

Extensions

Terms a(11) and beyond from Andrew Howroyd, Nov 24 2020