A370073 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, 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, 1, 18, 304, 2500, 6670, 1623, 1

Offset

1,9

Comments

The intermediate graphs may be disconnected.

See A370072 for further details.

Links

Table of n, a(n) for n=1..36.

Example

Triangle begins:
  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, 1, 18, 304, 2500, 6670, 1623, 1;
  ...

Crossrefs

Cf. A001349 (row sums), A370072.

Sequence in context: A318623 A332055 A073027 * A278986 A292159 A099793

Adjacent sequences: A370070 A370071 A370072 * A370074 A370075 A370076

Keyword

nonn,tabl,more

Author

Pontus von Brömssen, Feb 10 2024

Status

approved