A157282 Maximum cardinality of a weakly triple-free subset of {1, 2, ..., n}.

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, 21, 22, 23, 24, 25, 26, 26, 27, 28, 29, 30, 31, 31, 32, 33, 34, 35, 36, 36, 37, 38, 39, 40, 41, 41, 42, 43, 43, 44, 45, 45, 46, 47, 48, 49, 50, 50, 51, 52, 53, 54, 55, 55, 56, 57, 58, 59

Offset: 1

Author

Steven Finch, Feb 26 2009

Keywords

• nonn

Comments

A050294 is different from this sequence. A050294 involves sets encompassing no {x,3x}; this sequence involves sets encompassing no {x,2x,3x}.

From Steven Finch, Feb 27 2009: (Start)

Define d(n)=A003586(n), b(0)=0 and b(k)=A057561(n) for d(n) <= k < d(n+1).

Then a(n) = Sum_{m=1..ceiling(n/3)} b(floor(n/e(m))) where e(m) = A007310(m). (End)

Examples

			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.
		

Links

• Steven R. Finch, Triple-Free Sets of Integers [From Steven Finch, Apr 20 2019]

Crossrefs

A050296 is the strongly triple-free analog of this sequence.

Cf. A003586, A007310, A057561.

Extensions

More terms from Steven Finch, Feb 27 2009