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Search: id:A057750
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| A057750 |
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Number of non-factorable subsets of size >= 2 of a 1 X n uniform grid. |
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+0
3
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| 0, 1, 4, 10, 23, 49, 100, 202, 413, 839, 1713, 3493, 7130, 14535, 29617, 60158, 122077, 247132, 499409, 1007440, 2029801, 4083888, 8208828, 16484742
(list; graph; listen)
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OFFSET
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1,3
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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) and there are seven subsets with fewer than 2 elements, so a(6)=2^6-8-7=49.
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CROSSREFS
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Cf. A057765.
Sequence in context: A084446 A158671 A001980 this_sequence A118645 A137531 A159347
Adjacent sequences: A057747 A057748 A057749 this_sequence A057751 A057752 A057753
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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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