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A001434
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Number of graphs with n nodes and n edges.
(Formerly M1653 N0647)
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16
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1, 0, 0, 1, 2, 6, 21, 65, 221, 771, 2769, 10250, 39243, 154658, 628635, 2632420, 11353457, 50411413, 230341716, 1082481189, 5228952960, 25945377057, 132140242356, 690238318754, 3694876952577, 20252697246580, 113578669178222, 651178533855913, 3813856010041981
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listen;
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OFFSET
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0,5
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COMMENTS
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REFERENCES
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J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 146.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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EXAMPLE
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Representatives of the a(0) = 1 through a(5) = 6 graphs:
{} . . {12,13,23} {12,13,14,23} {12,13,14,15,23}
{12,13,24,34} {12,13,14,23,24}
{12,13,14,23,25}
{12,13,14,23,45}
{12,13,14,25,35}
{12,13,24,35,45}
(End)
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MATHEMATICA
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(* first do *) Needs["Combinatorica`"] (* then *) Table[ NumberOfGraphs[n, n], {n, 24}] (* Robert G. Wilson v, Mar 22 2011 *)
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 /@ Subsets[Subsets[Range[n], {2}], {n}]]], {n, 0, 5}] (* Gus Wiseman, Feb 22 2024 *)
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PROG
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CROSSREFS
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KEYWORD
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nonn,easy,nice
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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