A325108 Number of maximal subsets of {1...n} with no binary containments.

1, 1, 1, 2, 2, 4, 5, 6, 6, 11, 13, 16, 17, 22, 27, 28

Offset: 0

Author

Gus Wiseman, Mar 28 2019

Keywords

• nonn
• more

Comments

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.

Examples

			The a(0) = 1 through a(7) = 6 maximal subsets:
  {}  {1}  {1,2}  {3}    {3,4}    {2,5}    {1,6}    {7}
                  {1,2}  {1,2,4}  {3,4}    {2,5}    {1,6}
                                  {3,5}    {3,4}    {2,5}
                                  {1,2,4}  {1,2,4}  {3,4}
                                           {3,5,6}  {1,2,4}
                                                    {3,5,6}
		

Crossrefs

Cf. A006126, A014466, A019565, A267610.

Cf. A325095, A325096, A325101, A325106, A325107, A325109, A325110.

Programs

Mathematica

binpos[n_]:=Join@@Position[Reverse[IntegerDigits[n,2]],1];
stableQ[u_,Q_]:=!Apply[Or,Outer[#1=!=#2&&Q[#1,#2]&,u,u,1],{0,1}];
maxim[s_]:=Complement[s,Last/@Select[Tuples[s,2],UnsameQ@@#&&SubsetQ@@#&]];
Table[Length[maxim[Select[Subsets[Range[n]],stableQ[#,SubsetQ[binpos[#1],binpos[#2]]&]&]]],{n,0,10}]