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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
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
Sequence in context: A365681 A333665 A355595 * A330744 A330743 A362144
KEYWORD
nonn
AUTHOR
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 3 07:49 EST 2024. Contains 370499 sequences. (Running on oeis4.)