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%I #7 Sep 01 2019 08:41:15
%S 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,
%T 91,34,18,0,11,0,7403,2454,826,267,100,44,0,23,0,197442,48201,11383,
%U 2800,831,259,117,0,47,0
%N Triangle read by rows where T(n,k) is the number of unlabeled simple connected graphs with n vertices and k bridges.
%C 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).
%H Gus Wiseman, <a href="/A327077/a327077.png">Unlabeled connected graphs with 5 vertices and k bridges.</a>
%e Triangle begins:
%e 1
%e 1 0
%e 0 1 0
%e 1 0 1 0
%e 3 1 0 2 0
%e 11 4 3 0 3 0
%e 60 25 14 7 0 6 0
%e 502 197 91 34 18 0 11 0
%e 7403 2454 826 267 100 44 0 23 0
%e ...
%Y The labeled version is A327072.
%Y Row sums are A001349.
%Y Row sums without the k = 0 column are A052446.
%Y Column k = 0 is A007146, if we assume A007146(0) = 1.
%Y Column k = 1 is A327074.
%Y Column k = n - 1 is A000055.
%Y Cf. A002494, A327071, A327073, A327108, A327109, A327111, A327130, A327144, A327145, A327146.
%K nonn,more,tabl
%O 0,11
%A _Gus Wiseman_, Aug 26 2019
%E a(21)-a(54) from _Andrew Howroyd_, Aug 28 2019
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