A380240 Array read by antidiagonals: A(n,k) is the number of sensed planar maps with n vertices and k faces including one distinguished outside face, n >= 1, k >= 1.

1, 1, 2, 3, 1, 4, 12, 8, 2, 10, 48, 64, 25, 3, 26, 196, 412, 314, 78, 6, 80, 798, 2458, 2976, 1478, 270, 14, 246, 3248, 13452, 23588, 18844, 6748, 926, 34, 810, 13184, 70330, 166050, 192096, 110714, 30168, 3305, 95, 2704, 53416, 353716, 1074472, 1676668, 1397484, 613884, 132734, 11868, 280, 9252

Offset

1,3

Comments

The number of edges is n + k - 2.

Links

Table of n, a(n) for n=1..55.

Example

Array begins:
==============================================================
n\k |  1    2      3      4       5       6       7      8 ...
----+---------------------------------------------------------
  1 |  1    1      2      4      10      26      80    246 ...
  2 |  1    3     12     48     196     798    3248  13184 ...
  3 |  1    8     64    412    2458   13452   70330 353716 ...
  4 |  2   25    314   2976   23588  166050 1074472 ...
  5 |  3   78   1478  18844  192096 1676668 ...
  6 |  6  270   6748 110714 1397484 ...
  7 | 14  926  30168 613884 ...
  8 | 34 3305 132734 ...
   ...

Crossrefs

Columns 1..2 are A002995, A060404.

Rows 1..2 are A003239(n-1), A103943.

Antidiagonal sums are A103937.

Cf. A269920 (rooted), A379430 (sensed with no root).

Sequence in context: A079639 A104694 A125182 * A318685 A270312 A169625

Adjacent sequences: A380237 A380238 A380239 * A380241 A380242 A380243

Keyword

nonn,tabl

Author

Andrew Howroyd, Jan 21 2025

Status

approved