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

1,4

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

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

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).

Sequence in context: A232690 A143889 A350758 * A222940 A227120 A353343

Adjacent sequences: A241764 A241765 A241766 * A241768 A241769 A241770

Keyword

nonn

Author

Travis Hoppe and Anna Petrone, Apr 28 2014

Extensions

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

Status

approved