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%I #11 Nov 25 2019 00:58:24
%S 1,2,2,3,4,5,6,7,7,8,9,10,11,12,12,13,14,14,15,16,16,17,18,19,20,21,
%T 21,22,23,24,25,26,26,27,28,29,30,31,31,32,33,34,35,36,36,37,38,39,40,
%U 41,41,42,43,43,44,45,45,46,47,48,49,50,50,51,52,53,54,55,55,56,57,58,59
%N Maximum cardinality of a weakly triple-free subset of {1, 2, ..., n}.
%C A050294 is different from this sequence. A050294 involves sets encompassing no {x,3x}; this sequence involves sets encompassing no {x,2x,3x}.
%C From _Steven Finch_, Feb 27 2009: (Start)
%C Define d(n)=A003586(n), b(0)=0 and b(k)=A057561(n) for d(n) <= k < d(n+1).
%C Then a(n) = Sum_{m=1..ceiling(n/3)} b(floor(n/e(m))) where e(m) = A007310(m). (End)
%H Steven R. Finch, <a href="/FinchTriple.html">Triple-Free Sets of Integers</a> [From Steven Finch, Apr 20 2019]
%e a(9)=7 since there are three grid graphs, two with a single vertex {7}, {5} and the other with rows {1,3,9}, {2,6}, {4}, {8}. The upper triangles are removed by marking 2, 3.
%Y A050296 is the strongly triple-free analog of this sequence.
%Y Cf. A003586, A007310, A057561.
%K nonn
%O 1,2
%A _Steven Finch_, Feb 26 2009
%E More terms from _Steven Finch_, Feb 27 2009
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