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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. 7
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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified May 25 06:43 EDT 2022. Contains 354049 sequences. (Running on oeis4.)