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Triangle read by rows: T(n,k) is the number of unlabeled connected n-vertex graphs that are reachable in k (but no fewer) steps from the empty n-vertex graph, where a step consists of choosing a subset S of the vertices and replacing the subgraph induced by S by its complement, 0 <= k <= n-1.
1

%I #9 Feb 11 2024 16:50:24

%S 1,0,1,0,1,1,0,1,4,1,0,1,7,12,1,0,1,10,53,47,1,0,1,14,139,474,224,1,0,

%T 1,18,304,2500,6670,1623,1

%N Triangle read by rows: T(n,k) is the number of unlabeled connected n-vertex graphs that are reachable in k (but no fewer) steps from the empty n-vertex graph, where a step consists of choosing a subset S of the vertices and replacing the subgraph induced by S by its complement, 0 <= k <= n-1.

%C The intermediate graphs may be disconnected.

%C See A370072 for further details.

%e Triangle begins:

%e 1;

%e 0, 1;

%e 0, 1, 1;

%e 0, 1, 4, 1;

%e 0, 1, 7, 12, 1;

%e 0, 1, 10, 53, 47, 1;

%e 0, 1, 14, 139, 474, 224, 1;

%e 0, 1, 18, 304, 2500, 6670, 1623, 1;

%e ...

%Y Cf. A001349 (row sums), A370072.

%K nonn,tabl,more

%O 1,9

%A _Pontus von Brömssen_, Feb 10 2024