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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). 4
 1, 15, 10, 1, 70, 492, 690, 395, 105, 15, 1, 5040, 28595, 58905, 63990, 42392, 18732, 5880, 1330, 210, 21, 1, 16800, 442680, 2485920, 6629056, 10684723, 11716068, 9409806, 5824980, 2872317, 1147576, 373156, 98112, 20475, 3276 (list; graph; refs; listen; history; text; internal format)
 OFFSET 4,2 REFERENCES R. W. Robinson, Numerical implementation of graph counting algorithms, AGRC Grant, Math. Dept., Univ. Newcastle, Australia, 1977. T. R. S. Walsh, Counting labelled three-connected and homeomorphically irreducible two-connected graphs, J. Comb. Theory B (1982) 1-11, Table 1. LINKS R. W. Robinson, Rows 4 through 15, flattened (row 15 is incomplete). EXAMPLE Triangle begins: n = 4 k = 6 : 1 Total( 4) = 1 n = 5 k = 8 : 15 k = 9 : 10 k = 10 : 1 Total( 5) = 26 n = 6 k = 9 : 70 k = 10 : 492 k = 11 : 690 k = 12 : 395 k = 13 : 105 k = 14 : 15 k = 15 : 1 Total( 6) = 1768 n = 7 k = 11 : 5040 k = 12 : 28595 k = 13 : 58905 k = 14 : 63990 k = 15 : 42392 k = 16 : 18732 k = 17 : 5880 k = 18 : 1330 k = 19 : 210 k = 20 : 21 k = 21 : 1 Total( 7) = 225096 CROSSREFS Row sums give A005644. Cf. A123527, A123534. Sequence in context: A139725 A009929 A166523 * A215236 A040212 A299316 Adjacent sequences:  A123539 A123540 A123541 * A123543 A123544 A123545 KEYWORD nonn,tabf AUTHOR N. J. A. Sloane, Nov 13 2006 STATUS approved

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Last modified June 28 21:04 EDT 2022. Contains 354907 sequences. (Running on oeis4.)