A380632 Number of simple connected graphs on n unlabeled nodes with each node a member of exactly one cycle.

1, 0, 0, 1, 1, 1, 2, 2, 3, 5, 9, 14, 28, 49, 95, 182, 369, 733, 1509, 3103, 6504, 13627, 28949, 61701, 132457, 285454, 618863, 1346022, 2940287, 6444364, 14172744, 31257883, 69142445, 153333476, 340880766, 759549740, 1696122213, 3795178540, 8508326129, 19109193805, 42991993545, 96881110654

Offset

0,7

Comments

All such graphs are cactus graphs (with bridges allowed).

Links

Andrew Howroyd, Table of n, a(n) for n = 0..1000

Wikipedia, Cactus graph.

Index entries for sequences related to cacti.

Prog

(PARI) Vec(G(40)) \\ G() defined in A380631.

Crossrefs

Row sums of A380631.

Cf. A000083, A380805.

Sequence in context: A183559 A080553 A350432 * A226956 A141602 A153931

Adjacent sequences: A380628 A380629 A380631 * A380633 A380634 A380635

Keyword

nonn,new

Author

Andrew Howroyd, Feb 24 2025

Status

approved