A343873 Triangle read by rows: T(n,k) is the number of unlabeled connected planar graphs with n edges and k nodes (n >= 0, 1 <= k <= n + 1).

1, 0, 1, 0, 0, 1, 0, 0, 1, 2, 0, 0, 0, 2, 3, 0, 0, 0, 1, 5, 6, 0, 0, 0, 1, 5, 13, 11, 0, 0, 0, 0, 4, 19, 33, 23, 0, 0, 0, 0, 2, 22, 67, 89, 47, 0, 0, 0, 0, 1, 19, 107, 236, 240, 106, 0, 0, 0, 0, 0, 13, 130, 486, 797, 657, 235, 0, 0, 0, 0, 0, 5, 130, 804, 2075, 2678, 1806, 551

Offset: 0

Author

Andrew Howroyd, May 06 2021

Keywords

• nonn
• tabl

Comments

First differs from A054923 in row n=9.

Terms may be computed using the tools geng and planarg in nauty.

Examples

			Triangle begins (n edges >= 0, k vertices >= 1):
  1;
  0, 1;
  0, 0, 1;
  0, 0, 1, 2;
  0, 0, 0, 2, 3;
  0, 0, 0, 1, 5,  6;
  0, 0, 0, 1, 5, 13,  11;
  0, 0, 0, 0, 4, 19,  33,  23;
  0, 0, 0, 0, 2, 22,  67,  89,  47;
  0, 0, 0, 0, 1, 19, 107, 236, 240, 106;
  0, 0, 0, 0, 0, 13, 130, 486, 797, 657, 235;
  ...
		

Links

• Georg Grasegger, Table of n, a(n) for n = 0..285 (rows 0..22) (terms 0..209 (rows 0..19) from Andrew Howroyd)
• Brendan McKay and Adolfo Piperno, nauty and Traces

Crossrefs

Row sums are A046091.

Column sums are A003094.

Main diagonal is A000055.

Subsequent diagonals are A001429, A001435, A001436 (same as for not necessarily planar graphs).

Cf. A049334 (transpose), A054923, A343870.

Programs

nauty

geng -c $k $n:$n | planarg -q | countg -q # Georg Grasegger, Jul 06 2023