A341923 Array read by antidiagonals: T(n,k) is the number of 3-connected triangulations of a disk up to orientation-preserving isomorphisms with n interior nodes and k nodes on the boundary, n >= 1, k >= 3.

1, 1, 1, 1, 2, 5, 1, 2, 10, 24, 1, 3, 16, 60, 133, 1, 3, 28, 122, 386, 846, 1, 4, 39, 242, 925, 2652, 5661, 1, 4, 58, 419, 2039, 7066, 18914, 39556, 1, 5, 78, 711, 4101, 17138, 54560, 139264, 286000, 1, 5, 106, 1128, 7801, 38166, 142802, 426462, 1048947, 2123329

Offset

1,5

Comments

The initial terms of this sequence can also be computed using the tool "plantri", in particular the command "./plantri -u -v -o -P [n]" will compute values for a diagonal.

Links

Andrew Howroyd, Table of n, a(n) for n = 1..1275

G. Brinkmann and B. McKay, Plantri (program for generation of certain types of planar graph)

Example

Array begins:
=====================================================
n\k |     3      4      5       6       7       8
----+------------------------------------------------
  1 |     1      1      1       1       1       1 ...
  2 |     1      2      2       3       3       4 ...
  3 |     5     10     16      28      39      58 ...
  4 |    24     60    122     242     419     711 ...
  5 |   133    386    925    2039    4101    7801 ...
  6 |   846   2652   7066   17138   38166   79908 ...
  7 |  5661  18914  54560  142802  345099  782210 ...
  8 | 39556 139264 426462 1188412 3067938 7433635 ...
  ...

Prog

(PARI) A341923Array(8, 6) \\ See links in A342053 for program file.

Crossrefs

Columns k=3..6 are A002709, A341924, A341925, A341926.

Antidiagonal sums are A342052.

Cf. A262586 (2-connected), A341856 (rooted), A342053 (unrooted).

Sequence in context: A004575 A021402 A201890 * A146097 A091953 A228824

Adjacent sequences: A341920 A341921 A341922 * A341924 A341925 A341926

Keyword

nonn,tabl

Author

Andrew Howroyd, Feb 26 2021

Status

approved