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A325096 Number of maximal subsets of {1...n} with no binary carries.

%I A325096 #12 Jul 27 2019 14:57:51
%S A325096 1,1,1,2,2,3,4,5,5,7,9,10,12,13,14,15,15,20,25,27,32,34,36,37,42,44,
%T A325096 46,47,49,50,51,52,52,67,82,87,102,107,112,114,129,134,139,141,146,
%U A325096 148,150,151,166,171,176,178,183,185,187,188,193,195,197,198,200,201
%N A325096 Number of maximal subsets of {1...n} with no binary carries.
%C A325096 A binary carry of two positive integers is an overlap of the positions of 1's in their reversed binary expansion.
%H A325096 Alois P. Heinz, <a href="/A325096/b325096.txt">Table of n, a(n) for n = 0..8192</a>
%F A325096 a(2^n - 1) = A000110(n).
%e A325096 The a(1) = 1 through a(9) = 7 maximal subsets:
%e A325096   {1}  {12}  {3}   {34}   {25}   {16}   {7}    {78}    {69}
%e A325096              {12}  {124}  {34}   {25}   {16}   {168}   {78}
%e A325096                           {124}  {34}   {25}   {258}   {168}
%e A325096                                  {124}  {34}   {348}   {249}
%e A325096                                         {124}  {1248}  {258}
%e A325096                                                        {348}
%e A325096                                                        {1248}
%t A325096 binpos[n_]:=Join@@Position[Reverse[IntegerDigits[n,2]],1];
%t A325096 stableQ[u_,Q_]:=!Apply[Or,Outer[#1=!=#2&&Q[#1,#2]&,u,u,1],{0,1}];
%t A325096 maxim[s_]:=Complement[s,Last/@Select[Tuples[s,2],UnsameQ@@#&&SubsetQ@@#&]];
%t A325096 Table[Length[maxim[Select[Subsets[Range[n]],stableQ[#,Intersection[binpos[#1],binpos[#2]]!={}&]&]]],{n,0,10}]
%Y A325096 Cf. A000110, A019565, A050315, A080572, A247935, A267610, A267700.
%Y A325096 Cf. A325095, A325099, A325100, A325101, A325103, A325104, A325107.
%K A325096 nonn,look
%O A325096 0,4
%A A325096 _Gus Wiseman_, Mar 27 2019
%E A325096 a(15)-a(61) from _Alois P. Heinz_, Mar 28 2019