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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).

%I A343873 #14 Jul 07 2023 03:51:51
%S A343873 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 A343873 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 A343873 0,13,130,486,797,657,235,0,0,0,0,0,5,130,804,2075,2678,1806,551
%N 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).
%C A343873 First differs from A054923 in row n=9.
%C A343873 Terms may be computed using the tools geng and planarg in nauty.
%H A343873 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 A343873 Brendan McKay and Adolfo Piperno, <a href="http://pallini.di.uniroma1.it/">nauty and Traces</a>
%e A343873 Triangle begins (n edges >= 0, k vertices >= 1):
%e A343873   1;
%e A343873   0, 1;
%e A343873   0, 0, 1;
%e A343873   0, 0, 1, 2;
%e A343873   0, 0, 0, 2, 3;
%e A343873   0, 0, 0, 1, 5,  6;
%e A343873   0, 0, 0, 1, 5, 13,  11;
%e A343873   0, 0, 0, 0, 4, 19,  33,  23;
%e A343873   0, 0, 0, 0, 2, 22,  67,  89,  47;
%e A343873   0, 0, 0, 0, 1, 19, 107, 236, 240, 106;
%e A343873   0, 0, 0, 0, 0, 13, 130, 486, 797, 657, 235;
%e A343873   ...
%o A343873 (nauty) geng -c $k $n:$n | planarg -q | countg -q # _Georg Grasegger_, Jul 06 2023
%Y A343873 Row sums are A046091.
%Y A343873 Column sums are A003094.
%Y A343873 Main diagonal is A000055.
%Y A343873 Subsequent diagonals are A001429, A001435, A001436 (same as for not necessarily planar graphs).
%Y A343873 Cf. A049334 (transpose), A054923, A343870.
%K A343873 nonn,tabl
%O A343873 0,10
%A A343873 _Andrew Howroyd_, May 06 2021