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A123542 Triangular array T(n,k) giving number of 3-connected graphs with n labeled nodes and k edges (n >= 4, ceiling(3*n/2) <= k <= n(n-1)/2).

%I A123542 #12 May 23 2024 04:24:59
%S A123542 1,15,10,1,70,492,690,395,105,15,1,5040,28595,58905,63990,42392,18732,
%T A123542 5880,1330,210,21,1,16800,442680,2485920,6629056,10684723,11716068,
%U A123542 9409806,5824980,2872317,1147576,373156,98112,20475,3276
%N A123542 Triangular array T(n,k) giving number of 3-connected graphs with n labeled nodes and k edges (n >= 4, ceiling(3*n/2) <= k <= n(n-1)/2).
%D A123542 R. W. Robinson, Numerical implementation of graph counting algorithms, AGRC Grant, Math. Dept., Univ. Newcastle, Australia, 1977.
%H A123542 R. W. Robinson, <a href="/A123542/b123542.txt">Rows 4 through 15, flattened</a> (row 15 is incomplete).
%H A123542 T. R. S. Walsh, <a href="https://doi.org/10.1016/0095-8956(82)90072-7">Counting labeled three-connected and homeomorphically irreducible two-connected graphs</a>, J. Combin. Theory Ser. B 32 (1982), no. 1, 1-11, Table 1.
%e A123542 Triangle begins:
%e A123542 n = 4
%e A123542 k = 6 : 1
%e A123542 Total( 4) = 1
%e A123542 n = 5
%e A123542 k = 8 : 15
%e A123542 k = 9 : 10
%e A123542 k = 10 : 1
%e A123542 Total( 5) = 26
%e A123542 n = 6
%e A123542 k = 9 : 70
%e A123542 k = 10 : 492
%e A123542 k = 11 : 690
%e A123542 k = 12 : 395
%e A123542 k = 13 : 105
%e A123542 k = 14 : 15
%e A123542 k = 15 : 1
%e A123542 Total( 6) = 1768
%e A123542 n = 7
%e A123542 k = 11 : 5040
%e A123542 k = 12 : 28595
%e A123542 k = 13 : 58905
%e A123542 k = 14 : 63990
%e A123542 k = 15 : 42392
%e A123542 k = 16 : 18732
%e A123542 k = 17 : 5880
%e A123542 k = 18 : 1330
%e A123542 k = 19 : 210
%e A123542 k = 20 : 21
%e A123542 k = 21 : 1
%e A123542 Total( 7) = 225096
%Y A123542 Row sums give A005644. Cf. A123527, A123534.
%K A123542 nonn,tabf
%O A123542 4,2
%A A123542 _N. J. A. Sloane_, Nov 13 2006