This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A330345 #6 Dec 12 2019 09:33:37
%S A330345 0,0,1,6,42,700,16995
%N A330345 Number of labeled simple graphs with n vertices whose covered portion has exactly two automorphisms.
%e A330345 The a(4) = 42 graphs:
%e A330345 {12} {12,13} {12,13,24} {12,13,14,23}
%e A330345 {13} {12,14} {12,13,34} {12,13,14,24}
%e A330345 {14} {12,23} {12,14,23} {12,13,14,34}
%e A330345 {23} {12,24} {12,14,34} {12,13,23,24}
%e A330345 {24} {13,14} {12,23,34} {12,13,23,34}
%e A330345 {34} {13,23} {12,24,34} {12,14,23,24}
%e A330345 {13,34} {13,14,23} {12,14,24,34}
%e A330345 {14,24} {13,14,24} {12,23,24,34}
%e A330345 {14,34} {13,23,24} {13,14,23,34}
%e A330345 {23,24} {13,24,34} {13,14,24,34}
%e A330345 {23,34} {14,23,24} {13,23,24,34}
%e A330345 {24,34} {14,23,34} {14,23,24,34}
%t A330345 graprms[m_]:=Union[Table[Sort[Sort/@(m/.Rule@@@Table[{p[[i]],i},{i,Length[p]}])],{p,Permutations[Union@@m]}]];
%t A330345 Table[Length[Select[Subsets[Subsets[Range[n],{2}]],Length[graprms[#]]==Length[Union@@#]!/2&]],{n,0,4}]
%Y A330345 The unlabeled version is A330344.
%Y A330345 The covering case is A330297.
%Y A330345 Covering simple graphs are A006129.
%Y A330345 Graphs with exactly two automorphisms are A330297 (labeled covering), A330344 (unlabeled), A330345 (labeled), A330346 (unlabeled covering), A241454 (unlabeled connected).
%Y A330345 Cf. A006125, A143543, A330098, A330228, A330230, A330282, A330343.
%K A330345 nonn,more
%O A330345 0,4
%A A330345 _Gus Wiseman_, Dec 12 2019