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A365380
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Number of subsets of {1..n} that cannot be linearly combined using nonnegative coefficients to obtain n.
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24
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1, 1, 2, 2, 6, 4, 16, 12, 32, 32, 104, 48, 256, 208, 448, 448, 1568, 896, 3840, 2368, 6912, 7680, 22912, 10752, 50688, 44800, 104448, 88064, 324096, 165888, 780288, 541696, 1458176, 1519616, 4044800, 2220032, 10838016, 8744960, 20250624, 16433152, 62267392, 34865152
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OFFSET
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1,3
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LINKS
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FORMULA
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EXAMPLE
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The set {4,5,6} cannot be linearly combined to obtain 7 so is counted under a(7), but we have 8 = 2*4 + 0*5 + 0*6, so it is not counted under a(8).
The a(1) = 1 through a(8) = 12 subsets:
{} {} {} {} {} {} {} {}
{2} {3} {2} {4} {2} {3}
{3} {5} {3} {5}
{4} {4,5} {4} {6}
{2,4} {5} {7}
{3,4} {6} {3,6}
{2,4} {3,7}
{2,6} {5,6}
{3,5} {5,7}
{3,6} {6,7}
{4,5} {3,6,7}
{4,6} {5,6,7}
{5,6}
{2,4,6}
{3,5,6}
{4,5,6}
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MATHEMATICA
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combs[n_, y_]:=With[{s=Table[{k, i}, {k, y}, {i, 0, Floor[n/k]}]}, Select[Tuples[s], Total[Times@@@#]==n&]];
Table[Length[Select[Subsets[Range[n-1]], combs[n, #]=={}&]], {n, 5}]
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CROSSREFS
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A124506 appears to count combination-free subsets, differences of A326083.
A365046 counts combination-full subsets, first differences of A364914.
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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