A342060 Triangle read by rows: T(n,k) is the number of embeddings on the sphere of 2-connected planar graphs with n nodes and k faces, n >= 3, k=2..2*n-4.

1, 1, 1, 1, 1, 2, 4, 2, 1, 1, 3, 13, 21, 16, 5, 2, 1, 4, 29, 94, 183, 154, 76, 18, 5, 1, 6, 59, 328, 1146, 2114, 2144, 1246, 447, 88, 14, 1, 7, 104, 915, 5046, 16009, 30183, 33719, 23749, 10585, 3017, 489, 50, 1, 9, 181, 2239, 17876, 85550, 254831, 478913, 581324, 468388, 255156, 93028, 22077, 3071, 233

Offset: 3

Author

Andrew Howroyd, Mar 27 2021

Keywords

• nonn
• tabf

Comments

Equivalently, T(n,k) is the number of unsensed 2-connected 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 3..15 of this table.

Examples

			Triangle begins:
  1;
  1, 1,  1;
  1, 2,  4,   2,    1;
  1, 3, 13,  21,   16,    5,    2;
  1, 4, 29,  94,  183,  154,   76,   18,   5;
  1, 6, 59, 328, 1146, 2114, 2144, 1246, 447, 88, 14;
  ...
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 3..171 (rows 3..15)
• Gunnar Brinkmann and Brendan McKay, Fast generation of planar graphs (expanded edition), Tables 23-26.

Crossrefs

Row sums are A034889.

Cf. A006407 (by edges), A212438 (3-connected), A342059.

Formula

T(n,2) = 1.

T(n,3) = A253186(n-2).