%I #14 Jul 07 2023 03:51:51

%S 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,

%T 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,

%U 0,13,130,486,797,657,235,0,0,0,0,0,5,130,804,2075,2678,1806,551

%N 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).

%C First differs from A054923 in row n=9.

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

%H Georg Grasegger, <a href="/A343873/b343873.txt">Table of n, a(n) for n = 0..285 (rows 0..22)</a> (terms 0..209 (rows 0..19) from Andrew Howroyd)

%H Brendan McKay and Adolfo Piperno, <a href="http://pallini.di.uniroma1.it/">nauty and Traces</a>

%e Triangle begins (n edges >= 0, k vertices >= 1):

%e 1;

%e 0, 1;

%e 0, 0, 1;

%e 0, 0, 1, 2;

%e 0, 0, 0, 2, 3;

%e 0, 0, 0, 1, 5, 6;

%e 0, 0, 0, 1, 5, 13, 11;

%e 0, 0, 0, 0, 4, 19, 33, 23;

%e 0, 0, 0, 0, 2, 22, 67, 89, 47;

%e 0, 0, 0, 0, 1, 19, 107, 236, 240, 106;

%e 0, 0, 0, 0, 0, 13, 130, 486, 797, 657, 235;

%e ...

%o (nauty) geng -c $k $n:$n | planarg -q | countg -q # _Georg Grasegger_, Jul 06 2023

%Y Row sums are A046091.

%Y Column sums are A003094.

%Y Main diagonal is A000055.

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

%Y Cf. A049334 (transpose), A054923, A343870.

%K nonn,tabl

%O 0,10

%A _Andrew Howroyd_, May 06 2021