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

4,7

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

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.

Formula

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

Example

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
...

Crossrefs

Row and column sums are A119501.

Main diagonal is A342057.

The unsensed version is A212438.

Cf. A005645 (by edges).

Sequence in context: A152790 A247602 A201902 * A178609 A144948 A108335

Adjacent sequences: A239890 A239891 A239892 * A239894 A239895 A239896

Keyword

nonn,tabf

Author

N. J. A. Sloane, Apr 03 2014

Extensions

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

Status

approved