A372169 Number of unlabeled triangle-free graphs covering n vertices.

1, 0, 1, 1, 4, 7, 24, 69, 303, 1487, 10275, 92899, 1157109, 19534822, 447074367, 13764681083, 567227701549, 31139379910949

Offset: 0

Author

Gus Wiseman, Apr 23 2024

Keywords

• nonn
• more

Comments

The labeled version is A372168.

Examples

			Non-isomorphic representatives of the a(5) = 7 graphs:
  12-35-45
  13-24-35-45
  14-25-35-45
  15-25-35-45
  12-13-24-35-45
  15-23-24-35-45
  13-14-23-24-35-45
		

Links

• Eric Weisstein's World of Mathematics, Triangle-Free Graph
• Gus Wiseman, The a(6) = 24 unlabeled triangle-free graphs covering 6 vertices.

Crossrefs

Dominated by A002494, labeled A006129.

Covering case of A006785, labeled A213434.

The connected case is A024607.

For all cycles (not just triangles) we have A144958, labeled A105784.

The labeled version is A372168.

For a unique triangle (labeled) we have A372171, non-covering A372172.

Column k = 0 of A372173, labeled A372167.

For a unique triangle (unlabeled) we have A372174, non-covering A372194.

A001858 counts acyclic graphs, unlabeled A005195.

A006125 counts simple graphs, unlabeled A000088.

A054548 counts covering graphs by number of edges, unlabeled A370167.

A372170 counts graphs by triangles, unlabeled A263340.

Cf. A000055, A000272, A053530, A121251, A322700, A372175, A372191.

Formula

First differences of A006785.