

A005470


Number of unlabeled planar simple graphs with n nodes.
(Formerly M1252)


31



1, 1, 2, 4, 11, 33, 142, 822, 6966, 79853, 1140916, 18681008, 333312451
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OFFSET

0,3


COMMENTS

Euler transform of A003094.  Christian G. Bower


REFERENCES

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
W. T. Trotter, ed., Planar Graphs, Vol. 9, DIMACS Series in Discrete Mathematics and Theoretical Computer Science, Amer. Math. Soc., 1993.
Turner, James; Kautz, William H. A survey of progress in graph theory in the Soviet Union. SIAM Rev. 12 1970 suppl. iv+68 pp. MR0268074 (42 #2973). See p. 19.  N. J. A. Sloane, Apr 08 2014
Vetukhnovskii, F. Ya. "Estimate of the Number of Planar Graphs." In Soviet Physics Doklady, vol. 7, pp. 79. 1962.  From N. J. A. Sloane, Apr 08 2014
R. J. Wilson, Introduction to Graph Theory. Academic Press, NY, 1972, p. 162.


LINKS

Table of n, a(n) for n=0..12.
G. Brinkmann, and B. D. McKay, Fast generation of planar graphs, MATCH Commun. Math. Comput. Chem., 58 (2007) 323357.
Gunnar Brinkmann and Brendan McKay, plantri and fullgen programs for generation of certain types of planar graph.
Gunnar Brinkmann and Brendan McKay, plantri and fullgen programs for generation of certain types of planar graph [Cached copy, pdf file only, no active links, with permission]
E. Friedman, Illustration of small graphs
N. J. A. Sloane, Transforms
Eric Weisstein's World of Mathematics, Planar Graph
Index entries for "core" sequences


EXAMPLE

a(2) = 2 since o o and oo are the two planar simple graphs on two nodes.


MATHEMATICA

A003094 = {1, 1, 1, 2, 6, 20, 99, 646, 5974, 71885, 1052805, 17449299, 313372298}; max = Length[A003094]1; b[n_] := A003094[[n+1]]; f[x_] = (a[0]=1) + Sum[a[n]*x^n, {n, 1, max}]  Product[1/(1x^n)^b[n], {n, 1, max}]; sf = Series[f[x], {x, 0, max}] // CoefficientList[#, x]&; Table[a[n], {n, 0, max}] /. Solve[Thread[sf == 0]][[1]] (* JeanFrançois Alcover, Apr 25 2013, after Christian G. Bower *)


CROSSREFS

Cf. A003094 (connected planar graphs), A034889, A039735 (planar graphs by nodes and edges).
Cf. A126201.
Sequence in context: A123469 A123448 A039707 * A123471 A123416 A123406
Adjacent sequences: A005467 A005468 A005469 * A005471 A005472 A005473


KEYWORD

nonn,core,nice,hard,more


AUTHOR

N. J. A. Sloane


EXTENSIONS

n=8 term corrected and n=9..11 terms calculated by Brendan McKay
Terms a(0)  a(10) confirmed by David Applegate and N. J. A. Sloane, Mar 09 2007
a(12) added by Vaclav Kotesovec after A003094 (computed by Brendan McKay), Dec 06 2014


STATUS

approved



