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%I #19 Jan 21 2024 19:30:35
%S 1,2,4,7,14,28,50,100,200,360,720,1440,2560,5120,10240,17920,35840,
%T 71680,130816,261632,523264,915712,1831424,3662848,6516608,13033216,
%U 26066432,46688768,93377536,186755072,333491200,666982400,1333964800,2334438400,4668876800
%N Number of subsets of {1, 2, ..., n} that do not contain a subset of the form {x, 2x, 3x}.
%C Such subsets are called weakly triple-free sets. A050295 is the strongly triple-free analog of this sequence. - _Steven Finch_, Mar 02 2009
%H Sean A. Irvine, <a href="/A068060/b068060.txt">Table of n, a(n) for n = 0..100</a> (terms 0..61 from Alois P. Heinz)
%H Steven R. Finch, <a href="/FinchTriple.html">Triple-Free Sets of Integers</a> [From Steven Finch, Apr 20 2019]
%H Sean A. Irvine, <a href="https://github.com/archmageirvine/joeis/blob/master/src/irvine/oeis/a068/A068060.java">Java program</a> (github)
%e 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.
%Y Cf. A050293.
%K nonn
%O 0,2
%A _David Wasserman_, Feb 14 2002
%E a(33)-a(34) from _Alois P. Heinz_, Jan 17 2019
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