A361412 Number of connected 3-regular multigraphs on 2n unlabeled nodes rooted at an unoriented edge (or loop), loops allowed.

1, 3, 12, 67, 441, 3464, 31616, 331997, 3961462, 53105424, 791237787, 12978022526, 232407307054, 4511887729886, 94385418177277, 2116529900006321, 50646269987874834, 1288091152941695791, 34697173459041347465, 986800102740080746702, 29548269236430810895013

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.

a(n) is also the number of connected multigraphs on 2*n+1 unlabeled nodes with one vertex of degree 2 and all others of degree 3, loops allowed.

Examples

			The a(1) = 3 multigraphs correspond to either a triple edge rooted on one of the edges or to a single edge with a loop at each end and rooted on either the edge or the loop.
		

Crossrefs

A361135 is the 4-regular version.

Cf. A005967 (unrooted), A129427, A361446, A361447, A361448.