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A239893 Irregular triangle read by rows: T(n,k) is the number of sensed 3-connected planar maps with n >= 4 faces and k >= 4 vertices.

%I A239893 #21 Mar 27 2021 22:49:56
%S A239893 1,0,1,1,0,1,3,2,2,0,0,2,11,16,10,6,0,0,2,16,69,127,128,60,17,0,0,0,
%T A239893 10,127,541,1188,1441,1032,386,73,0,0,0,6,128,1188,5096,11982,17265,
%U A239893 15466,8582,2652,389,0,0,0,0,60,1441,11982,50586,127765,206880,222472,158057,71980,18914,2274
%N A239893 Irregular triangle read by rows: T(n,k) is the number of sensed 3-connected planar maps with n >= 4 faces and k >= 4 vertices.
%C A239893 T(n,k) is the number of polyhedra with n faces and k vertices up to orientation preserving isomorphisms. The number of edges is n+k-2. - _Andrew Howroyd_, Mar 27 2021
%H A239893 Andrew Howroyd, <a href="/A239893/b239893.txt">Table of n, a(n) for n = 4..199</a> (rows 4..17)
%H A239893 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>, Table 9-11.
%H A239893 Timothy R. Walsh, <a href="https://doi.org/10.1016/j.disc.2004.08.036">Efficient enumeration of sensed planar maps</a>, Discrete Math. 293 (2005), no. 1-3, 263--289. MR2136069 (2006b:05062).
%H A239893 Timothy R. S. Walsh, <a href="https://doi.org/10.1016/0095-8956(82)90074-0">Counting nonisomorphic three-connected planar maps</a>, J. Combin. Theory Ser. B 32 (1982), no. 1, 33-44.
%F A239893 T(n,k) = T(k,n). - _Andrew Howroyd_, Mar 27 2021
%e A239893 Triangle begins:
%e A239893 1
%e A239893 0 1 1
%e A239893 0 1 3  2   2
%e A239893 0 0 2 11  16   10     6
%e A239893 0 0 2 16  69  127   128    60     17
%e A239893 0 0 0 10 127  541  1188  1441   1032    386     73
%e A239893 0 0 0  6 128 1188  5096 11982  17265  15466   8582   2652   389
%e A239893 0 0 0  0  60 1441 11982 50586 127765 206880 222472 158057 71980 18914 2274
%e A239893 ...
%Y A239893 Row and column sums are A119501.
%Y A239893 Main diagonal is A342057.
%Y A239893 The unsensed version is A212438.
%Y A239893 Cf. A005645 (by edges).
%K A239893 nonn,tabf
%O A239893 4,7
%A A239893 _N. J. A. Sloane_, Apr 03 2014
%E A239893 Terms a(67) and beyond from _Andrew Howroyd_, Mar 27 2021