%I A050293
%S A050293 2,4,6,12,24,36,72,144,240,480,960,1440,2880,5760,8640,17280,34560,
%T A050293 57600,115200,230400,345600,691200,1382400,2073600,4147200,8294400,
%U A050293 13271040,26542080,53084160,79626240,159252480,318504960
%N A050293 Number of 3-fold-free subsets of {1, 2, ..., n}.
%C A050293 A set is 3-fold-free if it does not contain any subset of the form {x, 
               3x}.
%D A050293 B. Reznick and R. Holzsager, r-fold free sets of positive integers, Math. 
               Magazine 68 (1995) 71-72.
%H A050293 S. R. Finch, <a href="http://algo.inria.fr/csolve/triple/">Triple-Free 
               Sets of Integers</a>
%H A050293 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               Triple-FreeSet.html">Link to a section of The World of Mathematics.</
               a>
%e A050293 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.
%Y A050293 Cf. A050291-A050296, A068060.
%Y A050293 Sequence in context: A141320 A134865 A140753 this_sequence A048115 A047151 
               A068010
%Y A050293 Adjacent sequences: A050290 A050291 A050292 this_sequence A050294 A050295 
               A050296
%K A050293 nonn
%O A050293 1,1
%A A050293 Eric Weisstein (eric(AT)weisstein.com)
%E A050293 More terms from David Wasserman (wasserma(AT)spawar.navy.mil), Feb 14 
               2002
%E A050293 Corrected and edited by S. R. Finch (Steven.Finch(AT)inria.fr), Feb 25 
               2009