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 A325108 #8 Jul 27 2019 14:57:51
%S A325108 1,1,1,2,2,4,5,6,6,11,13,16,17,22,27,28
%N A325108 Number of maximal subsets of {1...n} with no binary containments.
%C A325108 A pair of positive integers is a binary containment if the positions of 1's in the reversed binary expansion of the first are a subset of the positions of 1's in the reversed binary expansion of the second.
%e A325108 The a(0) = 1 through a(7) = 6 maximal subsets:
%e A325108 {} {1} {1,2} {3} {3,4} {2,5} {1,6} {7}
%e A325108 {1,2} {1,2,4} {3,4} {2,5} {1,6}
%e A325108 {3,5} {3,4} {2,5}
%e A325108 {1,2,4} {1,2,4} {3,4}
%e A325108 {3,5,6} {1,2,4}
%e A325108 {3,5,6}
%t A325108 binpos[n_]:=Join@@Position[Reverse[IntegerDigits[n,2]],1];
%t A325108 stableQ[u_,Q_]:=!Apply[Or,Outer[#1=!=#2&&Q[#1,#2]&,u,u,1],{0,1}];
%t A325108 maxim[s_]:=Complement[s,Last/@Select[Tuples[s,2],UnsameQ@@#&&SubsetQ@@#&]];
%t A325108 Table[Length[maxim[Select[Subsets[Range[n]],stableQ[#,SubsetQ[binpos[#1],binpos[#2]]&]&]]],{n,0,10}]
%Y A325108 Cf. A006126, A014466, A019565, A267610.
%Y A325108 Cf. A325095, A325096, A325101, A325106, A325107, A325109, A325110.
%K A325108 nonn,more
%O A325108 0,4
%A A325108 _Gus Wiseman_, Mar 28 2019