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A361447
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Number of connected 3-regular (cubic) multigraphs on 2n unlabeled nodes rooted at an unoriented edge (or loop) whose removal does not disconnect the graph, loops allowed.
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4
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1, 2, 9, 49, 338, 2744, 26025, 282419, 3463502, 47439030, 718618117, 11937743088, 215896959624, 4224096594516, 88919920910684, 2004237153640098, 48165411560792500, 1229462431057436457, 33221743136066636436, 947415638925100675208, 28436953641282225835143
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OFFSET
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0,2
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COMMENTS
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a(0) = 1 by convention. Loops add two to the degree of a node.
Instead of a rooted edge, the graph can be considered to have a pair of external legs (or half-edges). The external legs add 1 to the degree of a node, but do not contribute to the connectivity of the graph.
The 4-regular version of this sequence is A361135 since removing a single edge from a connected even degree regular graph cannot disconnect the graph.
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LINKS
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FORMULA
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G.f.: B(x) - x*(B(x)^2 + B(x^2))/2 where B(x) is the g.f. of A361412.
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EXAMPLE
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The illustrations in A352175 by R. J. Mathar show 1, 2, 9, and 49 connected graphs corresponding to the initial terms of this sequence.
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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