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A068060
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Number of subsets of {1, 2, ..., n} that do not contain a subset of the form {x, 2x, 3x}.
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2
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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
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OFFSET
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0,2
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COMMENTS
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Such subsets are called weakly triple-free sets. A050295 is the strongly triple-free analog of this sequence. [From Steven Finch, Mar 02 2009]
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LINKS
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Table of n, a(n) for n=0..32.
S. R. Finch, Triple-Free Sets of Integers
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EXAMPLE
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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.
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CROSSREFS
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Cf. A050293.
Sequence in context: A018692 A161713 A018330 * A057744 A210210 A113405
Adjacent sequences: A068057 A068058 A068059 * A068061 A068062 A068063
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KEYWORD
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easy,nonn
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AUTHOR
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David Wasserman, Feb 14 2002
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STATUS
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approved
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