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MATHEMATICA
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independentQ[collection_] := If[MemberQ[collection, Table[0, {nn}]] \[Or] !
DuplicateFreeQ[collection], False, Apply[And, Table[! MemberQ[ Map[Clip[Total[#]] &, Subsets[Drop[collection, {i}], {2, Length[collection]}]],
collection[[i]]], {i, 1, Length[collection]}]]]; Map[Total,
Map[Select[#, # > 0 &] &, able[Table[Length[Select[Subsets[Tuples[{0, 1}, nn], {i}], independentQ[#] &]], {i, 0, nn}], {nn, 0, 5}]]]
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