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MATHEMATICA
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Table[With[{g = GraphData[{"TriangularHoneycombObtuseKnight", n}]}, Count[Subgraph[g, #] & /@ Rest[Subsets[VertexList[g]]], _?ConnectedGraphQ]], {n, 5}]
Table[With[{g = GraphData[{"TriangularHoneycombObtuseKnight", n}]}, Total[Boole[ConnectedGraphQ[Subgraph[g, #]]] & /@ Rest[Subsets[VertexList[g]]]]], {n, 5}]
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