A378077 Triangle read by rows: T(n,k) is the number of embeddings on the sphere of planar graphs with n vertices and k faces having connectivity exactly 2 and minimum vertex degree at least 3, k=6..2n-5.

1, 1, 1, 3, 7, 2, 1, 8, 35, 60, 47, 12, 0, 5, 72, 307, 647, 652, 325, 59, 0, 3, 86, 776, 3395, 7647, 9582, 6654, 2442, 368, 0, 0, 45, 1041, 9091, 38876, 94278, 136628, 121204, 64232, 18916, 2363, 0, 0, 18, 827, 14407, 111076, 468211, 1192511, 1937266, 2049784, 1409199, 607746, 150161, 16253

Offset: 6

Author

Andrew Howroyd, Nov 15 2024

Keywords

• nonn
• tabf

Comments

The graphs are 2-connected, but not 3-connected. Graphs with minimum degree at least 3 are also called homeomorphically irreducible.

The number of edges is n + k - 2.

Examples

			Triangle begins:
  n\k| 6  7   8     9    10     11     12      13      14     15     16    17
-----+------------------------------------------------------------------------
   6 | 1, 1;
   7 | 1, 3,  7,    2;
   8 | 1, 8, 35,   60,   47,    12;
   9 | 0, 5, 72,  307,  647,   652,   325,     59;
  10 | 0, 3, 86,  776, 3395,  7647,  9582,   6654,   2442,   368;
  11 | 0, 0, 45, 1041, 9091, 38876, 94278, 136628, 121204, 64232, 18916, 2363;
  ...
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 6..95 (rows 6..14)

Crossrefs

Rows sums are A187927.

Antidiagonals sums give A187928.

Cf. A378075.

Formula

T(n,k) = A212438(n,k) - A378075(n,k).