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Search: id:A134063
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| A134063 |
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Let P(A) be the power set of an n-element set A. Then a(n) = the number of pairs of elements {x,y} of P(A) for which either 0) x and y are disjoint and for which x is not a subset of y and y is not a subset of x, or 1) x and y are intersecting and for which either x is a proper subset of y or y is a proper subset of x, or 2) x = y. |
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+0
1
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| 1, 2, 7, 26, 91, 302, 967, 3026, 9331, 28502, 86527, 261626, 788971, 2375102, 7141687, 21457826, 64439011, 193448102, 580606447, 1742343626, 5228079451
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OFFSET
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0,2
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FORMULA
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a(n) = (1/2)(3^(n+1) - 2^(n+2) + 3) = 3*StirlingS2(n+1,3) + StirlingS2(n+1,2) + 1.
a(n) = StirlingS2(n+2,3) + 1. - Ross La Haye (rlahaye(AT)new.rr.com), Jan 21 2008
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EXAMPLE
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a(2) = 7 because for P(A) = {{},{1},{2},{1,2}} we have for case 0
{{1},{2}}, and we have for case 1 {{1},{1,2}}, {2},{1,2}}, and we have for
case 2 {{},{}}, {{1},{1}}, {{2},{2}}, {{1,2},{1,2}}.
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CROSSREFS
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Cf. A000392, A028243, A000079.
Sequence in context: A091145 A000697 A027417 this_sequence A087448 A129273 A055988
Adjacent sequences: A134060 A134061 A134062 this_sequence A134064 A134065 A134066
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KEYWORD
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nonn
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AUTHOR
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Ross La Haye (rlahaye(AT)new.rr.com), Jan 11 2008
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