What is the number of graphs with unlabeled (non isolated) nodes and 3 labeled edges?

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The OEIS sequence A014500 is the number of graphs with unlabeled (non isolated) nodes and n labeled edges. I am trying to count the case for n=3. I have 1 graph (a triangle) with 3 nodes. 3 length 3 path graphs, 3 graphs containing a path of length 2 and a path of length 1, and 1 graph containing 3 paths of length 1. The OEIS sequence says there should be 9