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A364671
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Number of subsets of {1..n} containing all of their own first differences.
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7
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1, 2, 4, 6, 10, 14, 23, 34, 58, 96, 171, 302, 565, 1041, 1969, 3719, 7105, 13544, 25999, 49852, 95949, 184658, 356129, 687068, 1327540, 2566295, 4966449, 9617306, 18640098, 36150918, 70166056, 136272548, 264844111, 515036040, 1002211421, 1951345157, 3801569113
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,2
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LINKS
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EXAMPLE
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The subset {1,2,4,5,10,14} has differences (1,2,1,5,4) so is counted under a(14).
The a(0) = 1 through a(5) = 14 subsets:
{} {} {} {} {} {}
{1} {1} {1} {1} {1}
{2} {2} {2} {2}
{1,2} {3} {3} {3}
{1,2} {4} {4}
{1,2,3} {1,2} {5}
{2,4} {1,2}
{1,2,3} {2,4}
{1,2,4} {1,2,3}
{1,2,3,4} {1,2,4}
{1,2,3,4}
{1,2,3,5}
{1,2,4,5}
{1,2,3,4,5}
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MATHEMATICA
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Table[Length[Select[Subsets[Range[n]], SubsetQ[#, Differences[#]]&]], {n, 0, 10}]
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PROG
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(C++) See Links section.
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CROSSREFS
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For differences of all strict pairs we have A054519, for partitions A007862.
For "disjoint" instead of "subset" we have A364463, partitions A363260.
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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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