A384850 Triangle read by rows: T(n,k) is the number of unsensed simple planar maps with n edges and k vertices, 1 <= k <= n+1.

1, 0, 1, 0, 0, 1, 0, 0, 1, 2, 0, 0, 0, 2, 3, 0, 0, 0, 1, 7, 6, 0, 0, 0, 1, 7, 22, 12, 0, 0, 0, 0, 5, 42, 76, 27, 0, 0, 0, 0, 2, 49, 237, 271, 65, 0, 0, 0, 0, 1, 35, 442, 1293, 1001, 175, 0, 0, 0, 0, 0, 18, 510, 3539, 6757, 3765, 490

Offset

0,10

Comments

The planar maps considered here are connected.

The initial terms of this sequence can be computed using the tool "plantri", in particular the command "./plantri -u -v -c1 -p [n]" will compute values for a column.

Links

Andrew Howroyd, Table of n, a(n) for n = 0..135 (rows 0..15)

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

Example

Triangle begins:
  1;
  0, 1;
  0, 0, 1;
  0, 0, 1, 2;
  0, 0, 0, 2, 3;
  0, 0, 0, 1, 7,  6;
  0, 0, 0, 1, 7, 22,  12;
  0, 0, 0, 0, 5, 42,  76,   27;
  0, 0, 0, 0, 2, 49, 237,  271,   65;
  0, 0, 0, 0, 1, 35, 442, 1293, 1001, 175;
  ...

Crossrefs

Row sums are A006395.

Column sums are A372892.

Main diagonal is A006082.

Subdiagonal is A384967.

Cf. A054923 (graphs), A277741 (not necessarily simple), A342060 (2-connected), A212438 (3-connected), A384963 (version by number of vertices then faces).

Sequence in context: A175070 A343873 A054923 * A263145 A057108 A349435

Adjacent sequences: A384847 A384848 A384849 * A384851 A384852 A384853

Keyword

nonn,tabl

Author

Andrew Howroyd, Jun 13 2025

Status

approved