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A050291
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Number of double-free subsets of {1, 2, ..., n}.
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11
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2, 3, 6, 10, 20, 30, 60, 96, 192, 288, 576, 960, 1920, 2880, 5760, 9360, 18720, 28080, 56160, 93600, 187200, 280800, 561600, 898560, 1797120, 2695680, 5391360, 8985600, 17971200, 26956800, 53913600, 87091200, 174182400, 261273600
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| A set is double-free if it does not contain both x and 2x.
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REFERENCES
| Wang, E. T. H. ``On Double-Free Sets of Integers.'' Ars Combin. 28, 97-100, 1989.
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LINKS
| T. D. Noe, Table of n, a(n) for n=1..400
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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FORMULA
| a(n+1)=a(n)*Fib(b(2n)+2)/Fib(b(2n)+1), Fib = A000045, b = A007814.
a(n) = 2^n - A088808(n). - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Oct 19 2003
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CROSSREFS
| Cf. A050292-A050296.
Sequence in context: A005833 A001678 A113292 * A135452 A077027 A030436
Adjacent sequences: A050288 A050289 A050290 * A050292 A050293 A050294
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KEYWORD
| nonn,easy,nice
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AUTHOR
| Eric Weisstein (eric(AT)weisstein.com)
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EXTENSIONS
| Extended with formula by Christian G. Bower (bowerc(AT)usa.net), Sep 15 1999
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