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Search: id:A032263
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| A032263 |
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Number of ways to partition n labeled elements into 4 pie slices allowing the pie to be turned over; number of 2-element proper antichains of an n-element set. |
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+0
23
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| 0, 0, 0, 3, 30, 195, 1050, 5103, 23310, 102315, 437250, 1834503, 7597590, 31175235, 127067850, 515396703, 2083011870, 8396420955, 33779000850, 135696347703, 544527210150, 2183335871475, 8749027724250
(list; graph; listen)
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OFFSET
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1,4
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COMMENT
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A proper antichain is an antichain iff each two of its members have a non-empty intersection.
Let P(A) be the power set of an n-element set A. Then a(n+1) = the number of pairs of elements {x,y} of P(A) for which x and y are intersecting but for which x is not a subset of y and y is not a subset of x. This is just a different formulation of the alternative sequence description. - Ross La Haye (rlahaye(AT)new.rr.com), Jan 09 2008
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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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LINKS
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C. G. Bower, Transforms (2)
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FORMULA
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"DIJ[ 4 ]" (bracelet, indistinct, labeled, 4 parts) transform of 1, 1, 1, 1...
3*S(n,4) = (4^n-4*3^n+6*2^n-4)/8 . - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Feb 26 2008
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MAPLE
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A032263 := proc(n) (4^n-4*3^n+6*2^n-4)/8 ; end: seq(A032263(n), n=1..20) ; - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Feb 26 2008
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CROSSREFS
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Sequence in context: A013219 A013220 A132413 this_sequence A003771 A121100 A130546
Adjacent sequences: A032260 A032261 A032262 this_sequence A032264 A032265 A032266
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KEYWORD
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nonn,easy,nice
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AUTHOR
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Christian G. Bower (bowerc(AT)usa.net)
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EXTENSIONS
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Alternative description from Vladeta Jovovic, Goran Kilibarda, Zoran Maksimovic (vladeta(AT)eunet.rs)
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