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Search: id:A134168
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| A134168 |
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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 and y are intersecting and for which either x is a proper subset of y or y is a proper subset of x, or 3) x = y. |
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+0
1
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| 1, 3, 9, 30, 111, 438, 1779, 7290, 29871, 121998, 496299, 2011650, 8129031, 32769558, 131850819, 529745610, 2126058591, 8525561118, 34166421339, 136858609170, 548013994551
(list; graph; listen)
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OFFSET
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0,2
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REFERENCES
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Ross La Haye, Binary Relations on the Power Set of an n-Element Set, Journal of Integer Sequences, Vol. 12 (2009), Article 09.2.6. [From Ross La Haye (rlahaye(AT)new.rr.com), Feb 22 2009]
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FORMULA
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a(n) = (1/2)(4^n - 3^n + 3*2^n - 1) = 3*StirlingS2(n+1,4) + 2*StirlingS2(n+1,3) + 2*StirlingS2(n+1,2) + 1.
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EXAMPLE
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a(2) = 9 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}} and we have for case 3 {{},{}}, {{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, A028243, A000079.
Sequence in context: A151472 A107379 A117428 this_sequence A124427 A055730 A120018
Adjacent sequences: A134165 A134166 A134167 this_sequence A134169 A134170 A134171
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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 12 2008
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