A380805 Number of unlabeled simple connected graphs with n nodes of degree at most 3 and each node a member of exactly one cycle.

1, 0, 0, 1, 1, 1, 2, 2, 3, 4, 7, 10, 18, 27, 49, 81, 147, 256, 476, 858, 1612, 2991, 5676, 10729, 20575, 39423, 76232, 147602, 287518, 561195, 1100190, 2161552, 4261059, 8418035, 16675006, 33098322, 65844566, 131233923, 262066375, 524224509, 1050414569

Offset: 0

Author

Gordon Hamilton, Feb 23 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
• Wikipedia, Cactus graph.
• Index entries for sequences related to cacti.

Crossrefs

Row sums of A380633.

Cf. A000083, A001349, A317722, A380632 (nodes of any degree).

Programs

PARI

Vec(G(40)) \\ G() defined in A380633. - Andrew Howroyd, Feb 24 2025

Extensions

a(13) onwards from Andrew Howroyd, Feb 24 2025