A342059 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 up to orientation preserving isomorphisms, n >= 3, k=2..2*n-4.

1, 1, 1, 1, 1, 2, 5, 2, 1, 1, 3, 17, 31, 22, 6, 2, 1, 4, 42, 157, 318, 265, 123, 26, 6, 1, 6, 87, 576, 2128, 4009, 4055, 2332, 804, 147, 17, 1, 7, 161, 1664, 9659, 31252, 59244, 66289, 46521, 20604, 5743, 892, 73, 1, 9, 286, 4151, 34700, 168757, 505410, 952044, 1156127, 931227, 506318, 183980, 43180, 5876, 389

Offset: 3

Author

Andrew Howroyd, Mar 27 2021

Keywords

• nonn
• tabf

Comments

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,  5,   2,    1;
  1, 3, 17,  31,   22,    6,    2;
  1, 4, 42, 157,  318,  265,  123,   26,   6;
  1, 6, 87, 576, 2128, 4009, 4055, 2332, 804, 147, 17;
  ...
		

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 A342058.

Cf. A006406 (by edges), A239893 (3-connected), A342060.

Formula

T(n,2) = 1.

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