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A085489 a(n) is the number of subsets of {1,...,n} containing no solutions to x+y=z with x and y distinct (one version of "sum-free subsets"). 60
1, 2, 4, 7, 13, 22, 37, 61, 102, 162, 261, 410, 646, 1001, 1553, 2370, 3645, 5515, 8303, 12470, 18713, 27811, 41244, 60962, 89733, 131870, 192522, 281125, 408680, 593880, 855661, 1238592, 1779614, 2563476, 3660084, 5255913, 7473380, 10696444, 15137517 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
First differs from A151897 at a(7) = 61, A151897(7) = 60. The one subset counted under a(7) but not under A151897(7) is {1,2,4,7}. - Gus Wiseman, Jun 07 2019
LINKS
Fausto A. C. Cariboni, Table of n, a(n) for n = 0..75, (terms up to a(57) from Ben Burns)
Eric Weisstein's World of Mathematics, Sum-Free Set [Strictly speaking this link is not relevant, since it uses a different definition of "sum-free".]
FORMULA
a(n) = 2^n - A088809(n). - Reinhard Zumkeller, Oct 19 2003
EXAMPLE
From Gus Wiseman, Jun 07 2019: (Start)
The a(0) = 1 through a(4) = 13 subsets:
{} {} {} {} {}
{1} {1} {1} {1}
{2} {2} {2}
{1,2} {3} {3}
{1,2} {4}
{1,3} {1,2}
{2,3} {1,3}
{1,4}
{2,3}
{2,4}
{3,4}
{1,2,4}
{2,3,4}
The a(5) = 22 subsets:
{} {1} {1,2} {1,2,4}
{2} {1,3} {1,2,5}
{3} {1,4} {1,3,5}
{4} {1,5} {2,3,4}
{5} {2,3} {2,4,5}
{2,4} {3,4,5}
{2,5}
{3,4}
{3,5}
{4,5}
(End)
MATHEMATICA
Table[Length[Select[Subsets[Range[n]], Intersection[ #, Select[ Plus@@@ Subsets[ #, {2}], #<=n&]]=={}&]], {n, 0, 10}] (* Gus Wiseman, Jun 07 2019 *)
CROSSREFS
See A007865 for another version.
Sequence in context: A364465 A151897 A192758 * A101268 A188920 A281362
KEYWORD
nonn,nice
AUTHOR
Eric W. Weisstein, Jul 02 2003
EXTENSIONS
More terms from Reinhard Zumkeller, Jul 13 2003
Edited by David Wasserman, Apr 16 2008
a(0) = 1 prepended by Gus Wiseman, Jun 07 2019
STATUS
approved

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Last modified March 19 04:58 EDT 2024. Contains 370952 sequences. (Running on oeis4.)