|
|
A050293
|
|
Number of 3-fold-free subsets of {1, 2, ..., n}.
|
|
2
|
|
|
1, 2, 4, 6, 12, 24, 36, 72, 144, 240, 480, 960, 1440, 2880, 5760, 8640, 17280, 34560, 57600, 115200, 230400, 345600, 691200, 1382400, 2073600, 4147200, 8294400, 13271040, 26542080, 53084160, 79626240, 159252480, 318504960, 477757440, 955514880, 1911029760
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
COMMENTS
|
A set is 3-fold-free if it does not contain any subset of the form {x, 3x}.
|
|
REFERENCES
|
B. Reznick and R. Holzsager, r-fold free sets of positive integers, Math. Magazine 68 (1995) 71-72.
|
|
LINKS
|
|
|
EXAMPLE
|
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.
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|