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Number of maximal double-free subsets of {1..n}.
4

%I #10 Jun 15 2019 10:40:57

%S 1,1,2,2,2,2,4,4,6,6,12,12,12,12,24,24,32,32,64,64,64,64,128,128,192,

%T 192,384,384,384,384,768,768,960,960,1920,1920,1920,1920,3840,3840,

%U 5760,5760,11520,11520,11520,11520,23040,23040,30720,30720

%N Number of maximal double-free subsets of {1..n}.

%C A set is double-free if no element is twice any other element.

%H Charlie Neder, <a href="/A326115/b326115.txt">Table of n, a(n) for n = 0..1000</a>

%F From _Charlie Neder_, Jun 11 2019: (Start)

%F a(n) = Product {k < n/2} A000931(8+floor(log_2(n/(2k+1)))).

%F a(2k+1) = a(2k), a(8k+4) = a(8k+3). (End)

%e The a(1) = 1 through a(9) = 6 sets:

%e {1} {1} {13} {23} {235} {235} {2357} {13457} {134579}

%e {2} {23} {134} {1345} {256} {2567} {13578} {135789}

%e {1345} {13457} {14567} {145679}

%e {1456} {14567} {15678} {156789}

%e {23578} {235789}

%e {25678} {256789}

%t fasmax[y_]:=Complement[y,Union@@(Most[Subsets[#]]&/@y)];

%t Table[Length[fasmax[Select[Subsets[Range[n]],Intersection[#,2*#]=={}&]]],{n,0,10}]

%Y Cf. A000931, A007865, A050291, A103580, A120641, A308546, A320340, A323092.

%Y Cf. A325865, A326020, A326022, A326083.

%K nonn

%O 0,3

%A _Gus Wiseman_, Jun 06 2019

%E a(16)-a(49) from _Charlie Neder_, Jun 11 2019