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A039735 Triangle read by rows: T(n,k) = number of nonisomorphic unlabeled planar graphs with n >= 1 nodes and 0 <= k <= 3n-6 edges.

%I A039735 #17 Sep 04 2023 11:34:56
%S A039735 1,1,1,1,1,1,1,1,1,2,3,2,1,1,1,1,2,4,6,6,6,4,2,1,1,1,2,5,9,15,21,24,
%T A039735 24,20,13,5,2,1,1,2,5,10,21,41,65,97,130,144,135,98,51,16,5,1,1,2,5,
%U A039735 11,24,56,115,221,401,658,956,1217,1264,1042,631,275,72,14,1,1,2,5
%N A039735 Triangle read by rows: T(n,k) = number of nonisomorphic unlabeled planar graphs with n >= 1 nodes and 0 <= k <= 3n-6 edges.
%C A039735 Planar graphs with n >= 3 nodes have at most 3n-6 edges. - _Charles R Greathouse IV_, Feb 18 2013
%D A039735 R. C. Read and R. J. Wilson, An Atlas of Graphs, Oxford, 1998.
%D A039735 R. J. Wilson, Introduction to Graph Theory. Academic Press, NY, 1972, p. 162.
%H A039735 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 A039735 From _Michael Somos_, Aug 23 2015: (Start)
%F A039735 Sum_{k} T(n, k) = A005470(n) if n >= 1.
%F A039735 log(1 + A(x, y)) = Sum_{n>0} B(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 A049334. (End)
%e A039735 Triangle starts
%e A039735 n\k 0  1  2  3  4  5  6  7  8  9 10 11 12
%e A039735 --:-- -- -- -- -- -- -- -- -- -- -- -- --
%e A039735 1:  1
%e A039735 2:  1  1
%e A039735 3:  1  1  1  1
%e A039735 4:  1  1  2  3  2  1  1
%e A039735 5:  1  1  2  4  6  6  6  4  2  1
%e A039735 6:  1  1  2  5  9 15 21 24 24 20 13  5  2
%Y A039735 Cf. A005470 (row sums), A008406, A049334.
%K A039735 nonn,tabf,nice
%O A039735 1,10
%A A039735 _Brendan McKay_