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A325111
Triangle read by rows: T(n,k) is the number of simple connected graphs on n unlabeled nodes with k articulation vertices, (0 <= k <= n).
7
1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 3, 2, 1, 0, 0, 10, 7, 3, 1, 0, 0, 56, 33, 17, 5, 1, 0, 0, 468, 244, 101, 32, 7, 1, 0, 0, 7123, 2792, 890, 242, 60, 9, 1, 0, 0, 194066, 52448, 11468, 2461, 527, 97, 12, 1, 0, 0, 9743542, 1690206, 239728, 35839, 6056, 1029, 155, 15, 1, 0, 0
OFFSET
0,11
COMMENTS
Articulation vertices are also called cutpoints. These are vertices that when removed increase the component count of the graph.
LINKS
Eric Weisstein's World of Mathematics, Articulation Vertex
EXAMPLE
Triangle begins:
1;
1 0;
1, 0, 0;
1, 1, 0, 0;
3, 2, 1, 0, 0;
10, 7, 3, 1, 0, 0;
56, 33, 17, 5, 1, 0, 0;
468, 244, 101, 32, 7, 1, 0, 0;
7123, 2792, 890, 242, 60, 9, 1, 0, 0;
...
CROSSREFS
Columns k=0..5 are A002218(n>1), A241767, A241768, A241769, A241770, A241771.
Row sums are A001349.
Cf. A327077, A370064 (labeled version).
Sequence in context: A221960 A171839 A257778 * A242928 A214845 A366766
KEYWORD
nonn,tabl
AUTHOR
Andrew Howroyd, Sep 05 2019
EXTENSIONS
Diagonal for k = n inserted by Andrew Howroyd, Feb 25 2024
STATUS
approved