This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A003094 M1652 #81 Feb 16 2025 08:32:27
%S A003094 1,1,1,2,6,20,99,646,5974,71885,1052805,17449299,313372298,5942258308
%N A003094 Number of unlabeled connected planar simple graphs with n nodes.
%C A003094 Inverse Euler transform of A005470. - _Christian G. Bower_, May 16 2003
%D A003094 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%D A003094 R. J. Wilson, Introduction to Graph Theory, Academic Press, NY, 1972, p. 162.
%H A003094 David Wasserman, Brendan McKay and Georg Grasegger, <a href="/A003094/b003094.txt">Table of n, a(n) for n = 0..13</a>
%H A003094 Steven R. Finch, <a href="https://doi.org/10.1017/9781316997741">Mathematical Constants II</a>, Encyclopedia of Mathematics and Its Applications, Cambridge University Press, Cambridge, 2018.
%H A003094 E. Friedman, <a href="/A000088/a000088a.gif">Illustration of small graphs</a>
%H A003094 Brendan McKay, <a href="http://users.cecs.anu.edu.au/~bdm/data/graphs.html">Planar graphs</a>
%H A003094 N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%H A003094 Peter Steinbach, <a href="/A000088/a000088_17.pdf">Field Guide to Simple Graphs, Volume 1</a>, Part 17 (For Volumes 1, 2, 3, 4 of this book see A000088, A008406, A000055, A000664, respectively.)
%H A003094 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PlanarConnectedGraph.html">Planar Connected Graph</a>
%e A003094 a(3) = 2 since the path o-o-o and the triangle are the two connected planar simple graphs on three nodes.
%t A003094 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 *)
%o A003094 (nauty) geng -c $n | planarg -q | countg -q # _Georg Grasegger_, Jul 06 2023
%Y A003094 Row sums of A049334.
%Y A003094 The labeled version is A096332.
%Y A003094 Cf. A005470, A126201.
%K A003094 nonn,nice,hard,more,core
%O A003094 0,4
%A A003094 _N. J. A. Sloane_
%E A003094 More terms from _Brendan McKay_
%E A003094 a(12) added by _Brendan McKay_, Dec 06 2014
%E A003094 a(13) added by _Georg Grasegger_, Jul 06 2023