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A327077
Triangle read by rows where T(n,k) is the number of unlabeled simple connected graphs with n vertices and k bridges.
10
1, 1, 0, 0, 1, 0, 1, 0, 1, 0, 3, 1, 0, 2, 0, 11, 4, 3, 0, 3, 0, 60, 25, 14, 7, 0, 6, 0, 502, 197, 91, 34, 18, 0, 11, 0, 7403, 2454, 826, 267, 100, 44, 0, 23, 0, 197442, 48201, 11383, 2800, 831, 259, 117, 0, 47, 0
OFFSET
0,11
COMMENTS
A bridge is an edge that, if removed without removing any incident vertices, disconnects the graph. Unlabeled connected graphs with no bridges are counted by A007146 (unlabeled graphs with spanning edge-connectivity >= 2).
EXAMPLE
Triangle begins:
1
1 0
0 1 0
1 0 1 0
3 1 0 2 0
11 4 3 0 3 0
60 25 14 7 0 6 0
502 197 91 34 18 0 11 0
7403 2454 826 267 100 44 0 23 0
...
CROSSREFS
The labeled version is A327072.
Row sums are A001349.
Row sums without the k = 0 column are A052446.
Column k = 0 is A007146, if we assume A007146(0) = 1.
Column k = 1 is A327074.
Column k = n - 1 is A000055.
Sequence in context: A051722 A357354 A166408 * A284826 A307752 A101548
KEYWORD
nonn,more,tabl
AUTHOR
Gus Wiseman, Aug 26 2019
EXTENSIONS
a(21)-a(54) from Andrew Howroyd, Aug 28 2019
STATUS
approved