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Search: id:A134045
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| A134045 |
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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 either x is a subset of y or y is a subset of x, or 1) x and y are intersecting but for which x is not a subset of y and y is not a subset of x, or 2) x = y. |
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+0
1
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| 1, 3, 7, 18, 61, 258, 1177, 5358, 23821, 103338, 439297, 1838598, 7605781, 31191618, 127100617, 515462238, 2083142941, 8396683098, 33779525137, 135697396278, 544529307301
(list; graph; listen)
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OFFSET
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0,2
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FORMULA
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a(n) = (1/2)(4^n - 3^(n+1) + 7*2^n - 3) = 3*StirlingS2(n+1,4) + 2*StirlingS2(n+1,2) + 1.
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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}}, {{},{1,2}} and we have for case 2 {{},{}}, {{1},{1}},
{{2},{2}}, {{1,2},{1,2}}. There are 0 {x,y} of P(A) in this example that
fall under case 1.
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CROSSREFS
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Cf. A000225, A032263, A000079.
Sequence in context: A103177 A062416 A110578 this_sequence A079898 A088629 A075609
Adjacent sequences: A134042 A134043 A134044 this_sequence A134046 A134047 A134048
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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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