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%I M0812 #31 Jan 05 2024 23:32:32
%S 1,2,3,6,16,42,151,596,2605,12098,59166,297684,1538590,8109078,
%T 43476751,236474942,1302680941,7256842362,40832979283,231838418310,
%U 1327095781740,7653155567834,44434752082990,259600430870176,1525366978752096,9010312253993072,53485145730576790
%N Number of sensed 2-connected (nonseparable) planar maps with n edges.
%C Some people begin this 2,1,2,3,6,..., others begin it 0,1,2,3,6,....
%C The dual of a nonseparable map is nonseparable, so the class of all nonseparable planar maps is self-dual. The maps considered here are unrooted and sensed and may include loops and parallel edges. - _Andrew Howroyd_, Mar 29 2021
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%D T. R. S. Walsh, personal communication.
%H Andrew Howroyd, <a href="/A006402/b006402.txt">Table of n, a(n) for n = 2..500</a>
%H V. A. Liskovets, T. R. S. Walsh, <a href="http://dx.doi.org/10.4153/CJM-1983-023-5">The enumeration of nonisomorphic 2-connected planar maps</a>, Canad. J. Math. 35 (1983), no. 3, 417-435.
%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.
%H T. R. S. Walsh, <a href="/A007401/a007401.pdf">Number of sensed planar maps with n edges and m vertices</a>
%o (PARI) \\ here r(n) is A000139(n-1).
%o r(n)={4*binomial(3*n,n)/(3*(3*n-2)*(3*n-1))}
%o a(n)={(r(n) + sumdiv(n, d, if(d<n, eulerphi(n/d)*binomial(3*d-1,2)*r(d))))/(2*n) + if(n%2, (n+1)*r((n+1)/2)/4, (3*n-4)*r(n/2)/16)} \\ _Andrew Howroyd_, Mar 29 2021
%Y Row sums of A342061.
%Y Cf. A000087 (with distinguished faces), A000139 (rooted), A005645, A006403 (unsensed), A006406 (without loops or parallel edges).
%K nonn
%O 2,2
%A _N. J. A. Sloane_
%E Terms a(23) and beyond from _Andrew Howroyd_, Mar 29 2021
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