A384964 Triangle read by rows: T(n,k) is the number of embeddings on the sphere of connected simple planar graphs with n nodes and k faces up to orientation preserving isomorphisms, n >= 1, k=1..max(1,2*n-4).

1, 1, 1, 1, 2, 2, 1, 1, 3, 8, 8, 6, 2, 1, 6, 29, 60, 73, 52, 25, 6, 2, 14, 113, 388, 768, 903, 728, 379, 136, 26, 6, 34, 444, 2303, 6584, 11782, 14321, 12113, 7298, 3048, 872, 147, 17, 95, 1763, 12650, 49806, 123547, 210314, 255884, 228807, 150929, 73428, 25536, 6142, 892, 73

Offset: 1

Author

Andrew Howroyd, Jun 13 2025

Keywords

• nonn
• tabf

Comments

Equivalently, T(n,k) is the number of sensed simple planar maps with n vertices and k faces.

The number of edges is n+k-2.

Terms of this sequence can be computed using the tool "plantri". The expanded reference gives rows 1..14 of this table.

Examples

			Triangle begins:
   1;
   1;
   1,   1,
   2,   2,    1,    1,
   3,   8,    8,    6,     2,     1,
   6,  29,   60,   73,    52,    25,     6,    2,
  14, 113,  388,  768,   903,   728,   379,  136,   26,   6,
  34, 444, 2303, 6584, 11782, 14321, 12113, 7298, 3048, 872, 147, 17;
  ...
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..158 (rows 1..14)
• Gunnar Brinkmann and Brendan McKay, Fast generation of planar graphs (expanded edition), Tables 19-22.

Crossrefs

Row sums are A384965.

Antidiagonal sums are A006394.

Columns 1..2 are A002995, A384966.

Cf. A379430 (not necessarily simple), A342059 (2-connected), A239893 (3-connected), A384963 (unsensed).