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A260217
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Number of base-3 n-digit pandigital numbers.
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3
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0, 0, 4, 24, 100, 360, 1204, 3864, 12100, 37320, 114004, 346104, 1046500, 3155880, 9500404, 28566744, 85831300, 257756040, 773792404, 2322425784, 6969374500, 20912317800, 62745342004, 188252803224, 564791964100, 1694443001160, 5083463221204, 15250658099064
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OFFSET
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1,3
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COMMENTS
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a(n+1) is the number of pairs (A,B) where A and B are nonempty subsets of {1,2,...,n} and one of these subsets is a proper subset of the other.
If "proper" is omitted, see A091344.
If empty subsets are included, see A027649 (all subsets) and A056182 (proper subsets). (End)
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LINKS
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FORMULA
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a(n) = 2*A028243(n) = 2*3^(n-1) - 2^(n+1) + 2.
G.f.: 4*x^3/((1-x)*(1-2*x)*(1-3*x)).
E.g.f.: 2/3*((exp(x)-1)^3).
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EXAMPLE
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a(3)=4 because, in base 3, there are four 3-digit pandigital numbers (11=102_3, 15=120_3, 19=201_3, and 21=210_3).
a(4)=24 because, in base 3, there are 24 4-digit pandigital numbers (1002_3, 1012_3, 1020_3, 1021_3, 1022_3, 1102_3, 1120_3, 1200_3, 1201_3, 1202_3, 1210_3, 1220_3, 2001_3, 2010_3, 2011_3, 2012_3, 2021_3, 2100_3, 2101_3, 2102_3, 2110_3, 2120_3, 2201_3, and 2210_3).
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MATHEMATICA
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PROG
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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