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A049334 Triangle read by rows: T(n, k) is the number of unlabeled connected planar simple graphs with n >= 1 nodes and 0<=k<=3*n-6 edges.

%I A049334 #20 Jul 11 2023 08:57:15
%S A049334 1,0,1,0,0,1,1,0,0,0,2,2,1,1,0,0,0,0,3,5,5,4,2,1,0,0,0,0,0,6,13,19,22,
%T A049334 19,13,5,2,0,0,0,0,0,0,11,33,67,107,130,130,96,51,16,5,0,0,0,0,0,0,0,
%U A049334 23,89,236,486,804,1112,1211,1026,626,275,72,14,0,0,0,0,0,0,0,0
%N A049334 Triangle read by rows: T(n, k) is the number of unlabeled connected planar simple graphs with n >= 1 nodes and 0<=k<=3*n-6 edges.
%C A049334 Planar graphs with n >= 3 nodes have at most 3*n-6 edges.
%H A049334 Georg Grasegger, <a href="/A049334/b049334.txt">Table of n, a(n) for n = 1..235 (rows 1..13)</a> (terms n = 1..147 (rows 1..11) from Andrew Howroyd)
%H A049334 F. Harary, <a href="http://dx.doi.org/10.1090/S0002-9947-1955-0068198-2">The number of linear, directed, rooted, and connected graphs</a>, Trans. Amer. Math. Soc. 78 (1955), 445-463. (MR0068198) See page 457, equation (2.9).
%F A049334 T(n, n-1) = A000055(n) and Sum_{k} T(n, k) = A003094(n) if n>=1. - _Michael Somos_, Aug 23 2015
%F A049334 log(1 + B(x, y)) = Sum{n>0} A(x^n, y^n) / n where A(x, y) = Sum_{n>0, k>=0} T(n,k) * x^n * y^k and similarly B(x, y) with A039735. - _Michael Somos_, Aug 23 2015
%e A049334 n\k 0  1  2  3  4  5  6  7  8  9 10 11 12
%e A049334 --:-- -- -- -- -- -- -- -- -- -- -- -- --
%e A049334 1:  1
%e A049334 2:  0  1
%e A049334 3:  0  0  1  1
%e A049334 4:  0  0  0  2  2  1  1
%e A049334 5:  0  0  0  0  3  5  5  4  2  1
%e A049334 6:  0  0  0  0  0  6 13 19 22 19 13  5  2
%o A049334 (nauty) geng -c $n $k:$k | planarg -q | countg -q # _Georg Grasegger_, Jul 11 2023
%Y A049334 Row sums are A003094.
%Y A049334 Column sums are A046091.
%Y A049334 Cf. A000055, A039735, A049336, A049337, A054924, A288265, A343873 (transpose).
%K A049334 nonn,tabf,nice
%O A049334 1,11
%A A049334 _Brendan McKay_