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

0,2

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.

Links

Table of n, a(n) for n=0..20.

Example

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.

Sequence in context: A375227 A289539 A370342 * A364620 A256125 A337059

Adjacent sequences: A361409 A361410 A361411 * A361413 A361414 A361415

Keyword

nonn

Author

Andrew Howroyd, Mar 12 2023

Status

approved