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Number of 2-connected planar maps with n edges (see reference for precise definition).
(Formerly M1195)
3

%I M1195 #24 Mar 28 2021 12:04:23

%S 1,1,2,4,9,24,81,274,1071,4357,18416,80040,356109,1610910,7399114

%N Number of 2-connected planar maps with n edges (see reference for precise definition).

%C Equivalently, a(n) is the number of embeddings on the sphere of 2-connected planar graphs with n edges up to orientation preserving isomorphisms. - _Andrew Howroyd_, Mar 27 2021

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H Timothy R. Walsh, <a href="http://dx.doi.org/10.1137/0604018">Generating nonisomorphic maps without storing them</a>, SIAM J. Algebraic Discrete Methods 4 (1983), no. 2, 161-178.

%F a(n) = Sum_{k=3..n} A342059(k, n+2-k). - _Andrew Howroyd_, Mar 27 2021

%Y Cf. A006402, A006404, A006407 (unsensed case), A342059.

%K nonn,more

%O 3,3

%A _N. J. A. Sloane_

%E a(11) and a(12) from _Sean A. Irvine_, Apr 02 2017

%E a(13)-a(17) from _Andrew Howroyd_, Mar 27 2021