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A370167
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Irregular triangle read by rows where T(n,k) is the number of unlabeled simple graphs covering n vertices with k = 0..binomial(n,2) edges.
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14
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1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 2, 2, 1, 1, 0, 0, 0, 1, 4, 5, 5, 4, 2, 1, 1, 0, 0, 0, 1, 3, 9, 15, 20, 22, 20, 14, 9, 5, 2, 1, 1, 0, 0, 0, 0, 1, 6, 20, 41, 73, 110, 133, 139, 126, 95, 64, 40, 21, 10, 5, 2, 1, 1, 0, 0, 0, 0, 1, 3, 15, 50, 124, 271, 515, 832, 1181, 1460, 1581, 1516, 1291, 970, 658, 400, 220, 114, 56, 24, 11, 5, 2, 1, 1
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graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,12
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LINKS
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EXAMPLE
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Triangle begins:
1
0
0 1
0 0 1 1
0 0 1 2 2 1 1
0 0 0 1 4 5 5 4 2 1 1
0 0 0 1 3 9 15 20 22 20 14 9 5 2 1 1
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MATHEMATICA
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brute[m_]:=First[Sort[Table[Sort[Sort /@ (m/.Rule@@@Table[{(Union@@m)[[i]], p[[i]]}, {i, Length[p]}])], {p, Permutations[Range[Length[Union@@m]]]}]]];
Table[Length[Union[brute /@ Select[Subsets[Subsets[Range[n], {2}], {k}], Union@@#==Range[n]&]]], {n, 0, 5}, {k, 0, Binomial[n, 2]}]
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PROG
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row(n)={Vecrev(G(n)-if(n>0, G(n-1)), binomial(n, 2)+1)}
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CROSSREFS
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KEYWORD
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nonn,tabf
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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