A326115 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,3

COMMENTS

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

LINKS

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

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)

EXAMPLE

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}

MATHEMATICA

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

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

CROSSREFS

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

Cf. A325865, A326020, A326022, A326083.

Sequence in context: A104976 A325710 A214927 * A355746 A239485 A237756

Adjacent sequences: A326112 A326113 A326114 * A326116 A326117 A326118

KEYWORD

nonn

AUTHOR

Gus Wiseman, Jun 06 2019

EXTENSIONS

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

STATUS

approved