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%I
%S 1,1,1,1,3,0,2,1,10,0,0,5,3,2,1,56,0,0,0,29,0,13,8,3,2,1,468,0,0,0,0,
%T 219,0,0,63,69,0,16,12,3,2,1,7123,0,0,0,0,0,2706,0,0,0,502,263,300,0,
%U 85,80,24,16,12,3,2,1,194066,0,0,0,0,0,0,52879,0,0,0,0,6191,3197,0,2148,861,632,319,352,132,160,80,24,21,12,3,2,1
%N Triangle T(n, k) of the number of connected graphs of order n with cutting number k >= 0.
%C The cutting number of a node v in a graph G is the number of pairs of nodes {u,w} of G such that u!=v, w!=v, and every path from u to w contains v. The cutting number of a connected graph, is the maximum cutting number of any node in the graph.
%H Sean A. Irvine, <a href="/A331422/b331422.txt">Rows n = 1..12 flattened</a>
%H Sean A. Irvine, <a href="https://github.com/archmageirvine/joeis/blob/master/src/irvine/oeis/a331/A331422.java">Java program</a> (github)
%H Simon Mukwembi and Senelani Dorothy Hove-Musekwa, <a href="https://doi.org/10.1007/s13226-012-0038-8">On bounds for the cutting number of a graph</a>, Indian J. Pure Appl. Math., 43 (2012), 637-649.
%e The triangle begins:
%e 1;
%e 1;
%e 1, 1;
%e 3, 0, 2, 1;
%e 10, 0, 0, 5, 3, 2, 1;
%e 56, 0, 0, 0, 29, 0, 13, 8, 3, 2, 1;
%e 468, 0, 0, 0, 0, 219, 0, 0, 63, 69, 0, 16, 12, 3, 2, 1;
%e ...
%e The length of row n is 1 + (n-1)*(n-2)/2.
%Y Cf. A331238 (trees), A001349 (row sums), A002218 (first column).
%K nonn,tabf
%O 1,5
%A _Sean A. Irvine_, Jan 16 2020
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