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.

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, 10, 127, 541, 1188, 1441, 1032, 386, 73, 0, 0, 0, 6, 128, 1188, 5096, 11982, 17265, 15466, 8582, 2652, 389, 0, 0, 0, 0, 60, 1441, 11982, 50586, 127765, 206880, 222472, 158057, 71980, 18914, 2274

Offset: 4

Author

N. J. A. Sloane, Apr 03 2014

Keywords

• nonn
• tabf

Comments

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

Examples

			Triangle begins:
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 10 127  541  1188  1441   1032    386     73
0 0 0  6 128 1188  5096 11982  17265  15466   8582   2652   389
0 0 0  0  60 1441 11982 50586 127765 206880 222472 158057 71980 18914 2274
...
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 4..199 (rows 4..17)
• Gunnar Brinkmann and Brendan McKay, Fast generation of planar graphs (expanded edition), Table 9-11.
• Timothy R. Walsh, Efficient enumeration of sensed planar maps, Discrete Math. 293 (2005), no. 1-3, 263--289. MR2136069 (2006b:05062).
• Timothy R. S. Walsh, Counting nonisomorphic three-connected planar maps, J. Combin. Theory Ser. B 32 (1982), no. 1, 33-44.

Crossrefs

Row and column sums are A119501.

Main diagonal is A342057.

The unsensed version is A212438.

Cf. A005645 (by edges).

Formula

T(n,k) = T(k,n). - Andrew Howroyd, Mar 27 2021

Extensions

Terms a(67) and beyond from Andrew Howroyd, Mar 27 2021