A361446 Number of connected 3-regular multigraphs on 2n unlabeled nodes rooted at an oriented edge (or loop), loops allowed.

1, 3, 16, 99, 717, 5964, 56701, 611750, 7432491, 100838222, 1514749135, 24989362186, 449429188211, 8754181791029, 183621843677724, 4126714250580949, 98932328702693666, 2520187379996442269, 67980528958530199837, 1935753445850303203221, 58025998739501873764826

Offset: 0

Author

Andrew Howroyd, Mar 12 2023

Keywords

• nonn

Comments

a(0) = 1 by convention. Loops add two to the degree of a node.

Crossrefs

A352174 is the 4-regular version.

Cf. A005967 (unrooted), A129427, A352175, A361412 (rooted at unoriented edge), A361447, A361448.

Formula

G.f.: B(x)/C(x) where B(x) is the g.f. of A352175 and C(x) is the g.f. of A129427.