%I #21 Mar 27 2021 22:49:56

%S 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 10,127,541,1188,1441,1032,386,73,0,0,0,6,128,1188,5096,11982,17265,

%U 15466,8582,2652,389,0,0,0,0,60,1441,11982,50586,127765,206880,222472,158057,71980,18914,2274

%N 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 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 Andrew Howroyd, <a href="/A239893/b239893.txt">Table of n, a(n) for n = 4..199</a> (rows 4..17)

%H 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 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 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 T(n,k) = T(k,n). - _Andrew Howroyd_, Mar 27 2021

%e Triangle begins:

%e 1

%e 0 1 1

%e 0 1 3 2 2

%e 0 0 2 11 16 10 6

%e 0 0 2 16 69 127 128 60 17

%e 0 0 0 10 127 541 1188 1441 1032 386 73

%e 0 0 0 6 128 1188 5096 11982 17265 15466 8582 2652 389

%e 0 0 0 0 60 1441 11982 50586 127765 206880 222472 158057 71980 18914 2274

%e ...

%Y Row and column sums are A119501.

%Y Main diagonal is A342057.

%Y The unsensed version is A212438.

%Y Cf. A005645 (by edges).

%K nonn,tabf

%O 4,7

%A _N. J. A. Sloane_, Apr 03 2014

%E Terms a(67) and beyond from _Andrew Howroyd_, Mar 27 2021