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%I #29 Jul 07 2023 03:51:10
%S 1,1,1,3,5,12,30,79,227,709,2318,8049,29372,112000,444855,1833072,
%T 7806724,34252145,154342391,712231465,3357126655,16119421175,
%U 78580665333
%N Number of connected planar graphs with n edges.
%C Inverse Euler transform of A343872. - _Andrew Howroyd_, May 05 2021
%H B. D. McKay and A. Piperno, <a href="http://dx.doi.org/10.1016/j.jsc.2013.09.003">Practical Graph Isomorphism</a>, II, J. Symbolic Computation, 60 (2014), pp. 94-112.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PlanarConnectedGraph.html">Planar Connected Graph.</a>
%e a(3) = 3 since the three connected graphs with three edges are a path, a triangle and a "Y".
%e The first difference between this sequence and A002905 is for n=9 edges where we see K_{3,3}, the "utility graph".
%o (nauty)
%o # count graphs for the sequence by number of vertices v, sum over v afterwards
%o geng -c $v $n:$n | planarg -q | countg -q # _Georg Grasegger_, Jul 06 2023
%Y Row sums of A343873.
%Y Column sums of A049334.
%Y Cf. A002905, A003094, A066951, A291842, A343869, A343872.
%K nonn,nice,hard,more
%O 0,4
%A _Brendan McKay_
%E a(11)-a(19) from _Martin Fuller_ using nauty by _Brendan McKay_, Mar 07 2015
%E a(20)-a(22) added by _Georg Grasegger_, Jul 06 2023
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