A381468 Number of simple connected graphs on n unlabeled nodes with no node a member of more than one cycle.

1, 1, 1, 2, 4, 8, 20, 48, 133, 374, 1124, 3439, 10923, 35245, 116128, 387729, 1312038, 4485906, 15486546, 53900520, 188998450, 667062919, 2368440477, 8454560144, 30328595227, 109285433191, 395425965732, 1436219868659, 5234881134074, 19143123415166, 70216752517419

Offset: 0

Author

Andrew Howroyd, Feb 24 2025

Keywords

• nonn

Comments

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

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..1000
• R. J. Mathar, Counting connected graphs without overlapping cycles, arXiv:1808.06264 [math.CO] (2018).
• Wikipedia, Cactus graph.
• Index entries for sequences related to cacti.

Crossrefs

Row sums of A381467.

Cf. A000083, A317722 (with 2-cycles), A380632, A380805.

Programs

PARI

Vec(G(31,1)) \\ G() defined in A381467.