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A323389

The number of connected, unlabeled, undirected, edge-signed cubic graphs (admitting loops and multiedges) on 2n vertices where the degree of the first sign is 2 at each node.

Obtained from the cubic graphs A005967 (connected undirected cubic graphs that may have loops and/or multiedges) by signing each edge with a plus or a minus such that two pluses and one minus meet at each vertex.