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A361412
Number of connected 3-regular multigraphs on 2n unlabeled nodes rooted at an unoriented edge (or loop), loops allowed.
3
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.
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
KEYWORD
nonn
AUTHOR
Andrew Howroyd, Mar 12 2023
STATUS
approved