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A085489
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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").
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60
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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
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OFFSET
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0,2
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COMMENTS
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LINKS
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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".]
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FORMULA
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EXAMPLE
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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)
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MATHEMATICA
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Table[Length[Select[Subsets[Range[n]], Intersection[ #, Select[ Plus@@@ Subsets[ #, {2}], #<=n&]]=={}&]], {n, 0, 10}] (* Gus Wiseman, Jun 07 2019 *)
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CROSSREFS
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KEYWORD
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nonn,nice
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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