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

0,10

Comments

First differs from A054923 in row n=9.

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

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

Example

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;
  ...

Prog

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

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.

Sequence in context: A275964 A284272 A175070 * A054923 A263145 A057108

Adjacent sequences: A343870 A343871 A343872 * A343874 A343875 A343876

Keyword

nonn,tabl

Author

Andrew Howroyd, May 06 2021

Status

approved