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Search: id:A057765
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| A057765 |
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Number of factorable subsets of a 1 X n uniform grid. |
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+0
3
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| 0, 0, 0, 1, 3, 8, 20, 45, 89, 174, 323, 590, 1048, 1834, 3135, 5361, 8977, 14993, 24859
(list; graph; listen)
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OFFSET
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1,5
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COMMENT
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A set is factorable if it is the union of at least two disjoint translated copies of a subset of at least two elements. E.g. the subset *..*.**..***.*.* of the 1x16 grid (where * denotes gridpoints in the selected subset and . denotes the remaining unselected gridpoints) is factorable into 3 copies of the 3-element subset *..*.*, as shown by displaying the factors by 1..1.12..232.3.3, where the numerals denote the elements of a particular translated copy.
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EXAMPLE
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The factorable subsets of (......) are (1122..), (11.22.), (.1122.), (1.12.2), (11..22), (.11.22), (..1122) and (111222), so a(6)=8.
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CROSSREFS
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Cf. A057750.
Sequence in context: A000236 A109327 A096585 this_sequence A134393 A014628 A034504
Adjacent sequences: A057762 A057763 A057764 this_sequence A057766 A057767 A057768
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KEYWORD
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nonn
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AUTHOR
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John W. Layman (layman(AT)math.vt.edu), Oct 30 2000
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