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A068060
Number of subsets of {1, 2, ..., n} that do not contain a subset of the form {x, 2x, 3x}.
3
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, 2334438400, 4668876800
OFFSET
0,2
COMMENTS
Such subsets are called weakly triple-free sets. A050295 is the strongly triple-free analog of this sequence. - Steven Finch, Mar 02 2009
LINKS
Sean A. Irvine, Table of n, a(n) for n = 0..100 (terms 0..61 from Alois P. Heinz)
Steven R. Finch, Triple-Free Sets of Integers [From Steven Finch, Apr 20 2019]
Sean A. Irvine, Java program (github)
EXAMPLE
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.
CROSSREFS
Cf. A050293.
Sequence in context: A018692 A161713 A018330 * A239791 A358837 A251653
KEYWORD
nonn
AUTHOR
David Wasserman, Feb 14 2002
EXTENSIONS
a(33)-a(34) from Alois P. Heinz, Jan 17 2019
STATUS
approved