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A003094 Number of unlabeled connected planar simple graphs with n nodes.
(Formerly M1652)
28
1, 1, 1, 2, 6, 20, 99, 646, 5974, 71885, 1052805, 17449299, 313372298, 5942258308 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,4
COMMENTS
Inverse Euler transform of A005470. - Christian G. Bower, May 16 2003
REFERENCES
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.
LINKS
David Wasserman, Brendan McKay and Georg Grasegger, Table of n, a(n) for n = 0..13
Steven R. Finch, Mathematical Constants II, Encyclopedia of Mathematics and Its Applications, Cambridge University Press, Cambridge, 2018.
Brendan McKay, Planar graphs
N. J. A. Sloane, Transforms
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.)
Eric Weisstein's World of Mathematics, Planar Connected Graph
EXAMPLE
a(3) = 2 since the path o-o-o and the triangle are the two connected planar simple graphs on three nodes.
MATHEMATICA
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 *)
PROG
(nauty) geng -c $n | planarg -q | countg -q # Georg Grasegger, Jul 06 2023
CROSSREFS
Row sums of A049334.
The labeled version is A096332.
Sequence in context: A020095 A026991 A049379 * A073964 A079457 A321911
KEYWORD
nonn,nice,hard,more,core
AUTHOR
EXTENSIONS
More terms from Brendan McKay
a(12) added by Brendan McKay, Dec 06 2014
a(13) added by Georg Grasegger, Jul 06 2023
STATUS
approved

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Last modified March 18 22:56 EDT 2024. Contains 370952 sequences. (Running on oeis4.)