A343870 Triangle read by rows: T(n,k) is the number of unlabeled nonseparable (or 2-connected) planar graphs with n edges and k nodes (n >= 1, 2 <= k <= n + 1).

1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 3, 3, 1, 0, 0, 0, 0, 2, 9, 4, 1, 0, 0, 0, 0, 1, 13, 20, 6, 1, 0, 0, 0, 0, 0, 11, 49, 40, 7, 1, 0, 0, 0, 0, 0, 5, 77, 158, 70, 9, 1, 0, 0, 0, 0, 0, 2, 75, 406, 426, 121, 11, 1, 0, 0, 0, 0, 0, 0, 47, 662, 1645, 1018, 189, 13, 1, 0

Offset: 1

Author

Andrew Howroyd, May 04 2021

Keywords

• nonn
• tabl

Examples

			Triangle T(n,k) begins (n edges >= 1, k vertices >= 2):
  1;
  0, 0;
  0, 1, 0;
  0, 0, 1, 0;
  0, 0, 1, 1,  0;
  0, 0, 1, 2,  1,  0;
  0, 0, 0, 3,  3,  1,   0;
  0, 0, 0, 2,  9,  4,   1,   0;
  0, 0, 0, 1, 13, 20,   6,   1,   0;
  0, 0, 0, 0, 11, 49,  40,   7,   1,  0;
  0, 0, 0, 0,  5, 77, 158,  70,   9,  1, 0;
  0, 0, 0, 0,  2, 75, 406, 426, 121, 11, 1, 0;
  ...
		

Links

• Georg Grasegger, Table of n, a(n) for n = 1..351 (26 rows) (first 210 terms (20 rows) from Andrew Howroyd)

Crossrefs

Row sums are A343869.

Column sums are A021103.

Cf. A049334, A049336 (transpose), A049337, A253186, A339070.

Programs

nauty

geng -C $k $n:$n | planarg -q | countg -q # Georg Grasegger, Jun 05 2023

Formula

T(n, n) = 1 for n >= 3.

T(n, n-1) = A253186(n-3) for n >= 3.