cp's OEIS Frontend

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

%I A372169 #7 Feb 16 2025 08:34:06
%S A372169 1,0,1,1,4,7,24,69,303,1487,10275,92899,1157109,19534822,447074367,
%T A372169 13764681083,567227701549,31139379910949
%N A372169 Number of unlabeled triangle-free graphs covering n vertices.
%C A372169 The labeled version is A372168.
%H A372169 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Triangle-FreeGraph.html">Triangle-Free Graph</a>
%H A372169 Gus Wiseman, <a href="/A372169/a372169.png">The a(6) = 24 unlabeled triangle-free graphs covering 6 vertices.</a>
%F A372169 First differences of A006785.
%e A372169 Non-isomorphic representatives of the a(5) = 7 graphs:
%e A372169   12-35-45
%e A372169   13-24-35-45
%e A372169   14-25-35-45
%e A372169   15-25-35-45
%e A372169   12-13-24-35-45
%e A372169   15-23-24-35-45
%e A372169   13-14-23-24-35-45
%Y A372169 Dominated by A002494, labeled A006129.
%Y A372169 Covering case of A006785, labeled A213434.
%Y A372169 The connected case is A024607.
%Y A372169 For all cycles (not just triangles) we have A144958, labeled A105784.
%Y A372169 The labeled version is A372168.
%Y A372169 For a unique triangle (labeled) we have A372171, non-covering A372172.
%Y A372169 Column k = 0 of A372173, labeled A372167.
%Y A372169 For a unique triangle (unlabeled) we have A372174, non-covering A372194.
%Y A372169 A001858 counts acyclic graphs, unlabeled A005195.
%Y A372169 A006125 counts simple graphs, unlabeled A000088.
%Y A372169 A054548 counts covering graphs by number of edges, unlabeled A370167.
%Y A372169 A372170 counts graphs by triangles, unlabeled A263340.
%Y A372169 Cf. A000055, A000272, A053530, A121251, A322700, A372175, A372191.
%K A372169 nonn,more
%O A372169 0,5
%A A372169 _Gus Wiseman_, Apr 23 2024