A343870 -id:A343870 - cp's OEIS frontend

A343869 Number of unlabeled nonseparable (or 2-connected) planar graphs with n edges.

1, 0, 1, 1, 2, 4, 7, 16, 41, 108, 320, 1042, 3575, 13064, 49938, 197729, 805991, 3363084, 14302891, 61813285, 270805177, 1200460492, 5376709415, 24302430375, 110745093999, 508380790741

Offset: 1

Andrew Howroyd, May 04 2021

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

Brendan McKay and Adolfo Piperno, nauty and Traces

Row sums of A343870.
Column sums of A049336(n > 1).
Cf. A002840 (3-connected), A010355, A021103, A046091, A289471, A291841.

# count graphs for the sequence by number of vertices v, sum over v afterwards
geng -C $v $n:$n | planarg -q | countg -q # Georg Grasegger, Jun 05 2023

a(21)-a(26) added by Georg Grasegger, Jun 05 2023

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).

Original entry on oeis.org

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

Andrew Howroyd, May 06 2021

First differs from A054923 in row n=9.

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

			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;
  ...

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

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.

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

cp's OEIS Frontend

A343869 Number of unlabeled nonseparable (or 2-connected) planar graphs with n edges.

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