|
Search: id:A157282
|
|
|
| A157282 |
|
Maximum cardinality of a weakly triple-free subset of {1, 2, ..., n}. |
|
+0
2
|
|
| 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
(list; graph; listen)
|
|
|
OFFSET
|
1,2
|
|
|
COMMENT
|
A050294 is different from this sequence. A050294 involves sets encompassing no {x,3x}; this sequence involves sets encompassing no {x,2x,3x}.
Contribution from S. R. Finch (Steven.Finch(AT)inria.fr), 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 b(floor(n/e(m))) where the summation is from m=1 to ceil(n/3) and where e(m)=A007310(m). (End)
|
|
LINKS
|
S. R. Finch, Triple-Free Sets of Integers
|
|
EXAMPLE
|
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.
|
|
CROSSREFS
|
A050296 is the strongly triple-free analog of this sequence.
Sequence in context: A038668 A071754 A078171 this_sequence A114010 A111633 A034138
Adjacent sequences: A157279 A157280 A157281 this_sequence A157283 A157284 A157285
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
S. R. Finch (Steven.Finch(AT)inria.fr), Feb 26 2009
|
|
EXTENSIONS
|
More terms from S. R. Finch (Steven.Finch(AT)inria.fr), Feb 27 2009
|
|
|
Search completed in 0.002 seconds
|
