|
| |
|
|
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.
|
|
6
|
|
|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
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
|
| |
|
|
