A050293 Number of 3-fold-free subsets of {1, 2, ..., n}.

1, 2, 4, 6, 12, 24, 36, 72, 144, 240, 480, 960, 1440, 2880, 5760, 8640, 17280, 34560, 57600, 115200, 230400, 345600, 691200, 1382400, 2073600, 4147200, 8294400, 13271040, 26542080, 53084160, 79626240, 159252480, 318504960, 477757440, 955514880, 1911029760

Offset: 0

Author

Eric W. Weisstein

Keywords

• nonn

Comments

A set is 3-fold-free if it does not contain any subset of the form {x, 3x}.

Examples

			a(6) = 36. There are 64 subsets of {1, 2, 3, 4, 5, 6}. We exclude the 16 that contain {1, 3} and the 16 that contain {2, 6}. We've double-counted the 4 that contain {1, 2, 3, 6}. This yields 64 - 16 - 16 + 4 = 36.
		

References

• B. Reznick and R. Holzsager, r-fold free sets of positive integers, Math. Magazine 68 (1995) 71-72.

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..3789
• Steven R. Finch, Triple-Free Sets of Integers [From Steven Finch, Apr 20 2019]
• Eric Weisstein's World of Mathematics, Triple-Free Set.

Crossrefs

Cf. A050291-A050296, A068060.

Extensions

More terms from David Wasserman, Feb 14 2002

Corrected and edited by Steven Finch, Feb 25 2009

a(0)=1 prepended by Alois P. Heinz, Jan 16 2019