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Number of two-connected (or biconnected) planar graphs with n nodes.
10

%I #28 Jun 07 2023 09:40:56

%S 0,0,0,1,3,9,44,294,2893,36496,545808,9029737,159563559,2952794985,

%T 56589742050

%N Number of two-connected (or biconnected) planar graphs with n nodes.

%C For n < 3, conventions vary: Read & Wilson set a(2) = 0, but Gagarin et al. set a(2) = 1. - _Andrey Zabolotskiy_, Jun 07 2023

%D R. C. Read and R. J. Wilson, An Atlas of Graphs, Oxford, 1998. See p. 229.

%H A. Gagarin, G. Labelle, P. Leroux, and T. Walsh, <a href="https://doi.org/10.1016/j.aam.2009.01.002">Structure and enumeration of two-connected graphs with prescribed three-connected components</a>, Adv. in Appl. Math. 43 (2009), no. 1, pp. 46-74. See (116) on p. 69.

%Y Row sums of A049336.

%Y The labeled version is A096331.

%Y Cf. A000944 (3-connected), A002218, A003094, A005470.

%K nonn,more

%O 0,5

%A _Brendan McKay_

%E a(12)-a(14) from Gilbert Labelle (labelle.gilbert(AT)uqam.ca), Jan 20 2009

%E Offset 0 from _Michel Marcus_, Jun 05 2023

%E a(2) changed back to 0 by _Georg Grasegger_ and _Andrey Zabolotskiy_, Jun 07 2023