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Search: id:A134064
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| A134064 |
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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 intersecting but 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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1
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| 1, 2, 6, 23, 96, 407, 1716, 7163, 29616, 121487, 495276, 2009603, 8124936, 32761367, 131834436, 529712843, 2125993056, 8525430047, 34166159196, 136858084883, 548012945976
(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 + 2^n + 1) = 3*StirlingS2(n+1,4) + 2*StirlingS2(n+1,3) + StirlingS2(n+1,2) + 1.
a(n) = C(2^n + 1,2) - (1/2)(3^n - 1) = StirlingS2(2^n + 1,2^n) - StirlingS2(n+1,3) - StirlingS2(n+1,2). - Ross La Haye (rlahaye(AT)new.rr.com), Jan 21 2008 Ross
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EXAMPLE
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a(2) = 6 because for P(A) = {{},{1},{2},{1,2}} 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}}. There are 0 {x,y} of P(A) in this example that
fall under case 0.
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CROSSREFS
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Cf. A032263, A028243, A000079.
Sequence in context: A150294 A150295 A150296 this_sequence A111283 A150297 A150298
Adjacent sequences: A134061 A134062 A134063 this_sequence A134065 A134066 A134067
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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 Ross
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