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A331238
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Triangle T(n, k) of the number of trees of order n with cutting number k >= 0.
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3
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1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 2, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 2, 3, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 3, 7, 2, 2, 3, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 4, 8, 4, 7, 7, 2, 3, 3, 1, 1, 1
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OFFSET
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1,23
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COMMENTS
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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 (including trees as considered here), is the maximum cutting number of any node in the graph.
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LINKS
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EXAMPLE
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Triangle begins:
1;
1;
0, 1;
0, 0, 1, 1;
0, 0, 0, 0, 1, 1, 1;
0, 0, 0, 0, 0, 0, 1, 2, 1, 1, 1;
0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 2, 3, 1, 1, 1;
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 3, 7, 2, 2, 3, 1, 1, 1;
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 4, 8, 4, 7, 7, 2, 3, 3, 1, 1, 1;
...
The smallest nonzero entry on each row occurs at n-2 and the maximum at (n-1)*(n-2)/2.
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CROSSREFS
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KEYWORD
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nonn,tabf
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AUTHOR
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STATUS
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approved
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