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A342060 Triangle read by rows: T(n,k) is the number of embeddings on the sphere of 2-connected planar graphs with n nodes and k faces, n >= 3, k=2..2*n-4.

%I A342060 #11 Mar 28 2021 14:23:37
%S A342060 1,1,1,1,1,2,4,2,1,1,3,13,21,16,5,2,1,4,29,94,183,154,76,18,5,1,6,59,
%T A342060 328,1146,2114,2144,1246,447,88,14,1,7,104,915,5046,16009,30183,33719,
%U A342060 23749,10585,3017,489,50,1,9,181,2239,17876,85550,254831,478913,581324,468388,255156,93028,22077,3071,233
%N A342060 Triangle read by rows: T(n,k) is the number of embeddings on the sphere of 2-connected planar graphs with n nodes and k faces, n >= 3, k=2..2*n-4.
%C A342060 Equivalently, T(n,k) is the number of unsensed 2-connected planar maps with n vertices and k faces.
%C A342060 The number of edges is n+k-2.
%C A342060 Terms of this sequence can be computed using the tool "plantri". The expanded reference gives rows 3..15 of this table.
%H A342060 Andrew Howroyd, <a href="/A342060/b342060.txt">Table of n, a(n) for n = 3..171</a> (rows 3..15)
%H A342060 Gunnar Brinkmann and Brendan McKay, <a href="https://users.cecs.anu.edu.au/~bdm/papers/plantri-full.pdf">Fast generation of planar graphs (expanded edition)</a>, Tables 23-26.
%F A342060 T(n,2) = 1.
%F A342060 T(n,3) = A253186(n-2).
%e A342060 Triangle begins:
%e A342060   1;
%e A342060   1, 1,  1;
%e A342060   1, 2,  4,   2,    1;
%e A342060   1, 3, 13,  21,   16,    5,    2;
%e A342060   1, 4, 29,  94,  183,  154,   76,   18,   5;
%e A342060   1, 6, 59, 328, 1146, 2114, 2144, 1246, 447, 88, 14;
%e A342060   ...
%Y A342060 Row sums are A034889.
%Y A342060 Cf. A006407 (by edges), A212438 (3-connected), A342059.
%K A342060 nonn,tabf
%O A342060 3,6
%A A342060 _Andrew Howroyd_, Mar 27 2021