A326115 Number of maximal double-free subsets of {1..n}.

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, 192, 384, 384, 384, 384, 768, 768, 960, 960, 1920, 1920, 1920, 1920, 3840, 3840, 5760, 5760, 11520, 11520, 11520, 11520, 23040, 23040, 30720, 30720

Offset: 0

Author

Gus Wiseman, Jun 06 2019

Keywords

• nonn

Comments

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

Examples

			The a(1) = 1 through a(9) = 6 sets:
  {1}  {1}  {13}  {23}   {235}   {235}   {2357}   {13457}  {134579}
       {2}  {23}  {134}  {1345}  {256}   {2567}   {13578}  {135789}
                                 {1345}  {13457}  {14567}  {145679}
                                 {1456}  {14567}  {15678}  {156789}
                                                  {23578}  {235789}
                                                  {25678}  {256789}
		

Links

• Charlie Neder, Table of n, a(n) for n = 0..1000

Crossrefs

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

Cf. A325865, A326020, A326022, A326083.

Programs

Mathematica

fasmax[y_]:=Complement[y,Union@@(Most[Subsets[#]]&/@y)];
Table[Length[fasmax[Select[Subsets[Range[n]],Intersection[#,2*#]=={}&]]],{n,0,10}]

Formula

From Charlie Neder, Jun 11 2019: (Start)

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

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

Extensions

a(16)-a(49) from Charlie Neder, Jun 11 2019