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A050293
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Number of 3-fold-free subsets of {1, 2, ..., n}.
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1
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| A set is 3-fold-free if it does not contain any subset of the form {x, 3x}.
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REFERENCES
| B. Reznick and R. Holzsager, r-fold free sets of positive integers, Math. Magazine 68 (1995) 71-72.
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LINKS
| S. R. Finch, Triple-Free Sets of Integers
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
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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.
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CROSSREFS
| Cf. A050291-A050296, A068060.
Sequence in context: A141320 A134865 A140753 * A048115 A047151 A068010
Adjacent sequences: A050290 A050291 A050292 * A050294 A050295 A050296
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KEYWORD
| nonn
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AUTHOR
| Eric Weisstein (eric(AT)weisstein.com)
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EXTENSIONS
| More terms from David Wasserman (wasserma(AT)spawar.navy.mil), Feb 14 2002
Corrected and edited by S. R. Finch (Steven.Finch(AT)inria.fr), Feb 25 2009
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