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A050293 Number of 3-fold-free subsets of {1, 2, ..., n}. 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

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

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..95

Steven R. Finch, Triple-Free Sets of Integers [From Steven Finch, Apr 20 2019]

Eric Weisstein's World of Mathematics, Triple-Free Set.

EXAMPLE

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.

CROSSREFS

Cf. A050291-A050296, A068060.

Sequence in context: A328519 A234517 A236021 * A330744 A330743 A244896

Adjacent sequences:  A050290 A050291 A050292 * A050294 A050295 A050296

KEYWORD

nonn

AUTHOR

Eric W. Weisstein

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

STATUS

approved

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Last modified March 30 10:09 EDT 2020. Contains 333125 sequences. (Running on oeis4.)