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A003094
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Number of unlabeled connected planar simple graphs with n nodes.
(Formerly M1652)
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28
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1, 1, 1, 2, 6, 20, 99, 646, 5974, 71885, 1052805, 17449299, 313372298, 5942258308
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,4
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COMMENTS
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
R. J. Wilson, Introduction to Graph Theory, Academic Press, NY, 1972, p. 162.
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LINKS
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Steven R. Finch, Mathematical Constants II, Encyclopedia of Mathematics and Its Applications, Cambridge University Press, Cambridge, 2018.
Peter Steinbach, Field Guide to Simple Graphs, Volume 1, Part 17 (For Volumes 1, 2, 3, 4 of this book see A000088, A008406, A000055, A000664, respectively.)
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EXAMPLE
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a(3) = 2 since the path o-o-o and the triangle are the two connected planar simple graphs on three nodes.
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MATHEMATICA
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a[n_Integer?NonNegative] := a[n] = Module[{m, s, g}, s = Subsets[Range[n], {2}]; m = Length[s]; g = Graph[Range[n], UndirectedEdge @@@ #] & /@ (Pick[s, #, 1] & /@ (IntegerDigits[#, 2, m] & /@ Range[0, 2^m - 1])); Length[DeleteDuplicates[Select[Select[g, ConnectedGraphQ], PlanarGraphQ], IsomorphicGraphQ]]]; Table[a[n], {n, 0, 6}] (* Robert P. P. McKone, Oct 14 2023 *)
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PROG
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CROSSREFS
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KEYWORD
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nonn,nice,hard,more,core
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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