A068060 Number of subsets of {1, 2, ..., n} that do not contain a subset of the form {x, 2x, 3x}.

1, 2, 4, 7, 14, 28, 50, 100, 200, 360, 720, 1440, 2560, 5120, 10240, 17920, 35840, 71680, 130816, 261632, 523264, 915712, 1831424, 3662848, 6516608, 13033216, 26066432, 46688768, 93377536, 186755072, 333491200, 666982400, 1333964800, 2334438400, 4668876800

Offset: 0

Author

David Wasserman, Feb 14 2002

Keywords

• nonn

Comments

Such subsets are called weakly triple-free sets. A050295 is the strongly triple-free analog of this sequence. - Steven Finch, Mar 02 2009

Examples

			a(6) = 50. There are 64 subsets of {1, 2, 3, 4, 5, 6}. We exclude the 8 that contain {1, 2, 3} and the 8 that contain {2, 4, 6}. We've double-counted the 2 that contain {1, 2, 3, 4, 6}. This yields 64 - 8 - 8 + 2 = 50.
		

Links

• Sean A. Irvine, Table of n, a(n) for n = 0..100 (terms 0..61 from Alois P. Heinz)
• Steven R. Finch, Triple-Free Sets of Integers [From Steven Finch, Apr 20 2019]
• Sean A. Irvine, Java program (github)

Crossrefs

Cf. A050293.

Extensions

a(33)-a(34) from Alois P. Heinz, Jan 17 2019