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A083670
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Number of different antisymmetric relations on n unlabeled points.
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3
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1, 2, 7, 44, 558, 16926, 1319358, 269695440, 146202099255, 212360894456310, 834625722216941739, 8954592469138636320960, 264305834899495393164591240, 21607243912704793462806305720502, 4921054357098031770205099867497197328
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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LINKS
| G. Pfeiffer, Counting Transitive Relations, Journal of Integer Sequences, Vol. 7 (2004), Article 04.3.2.
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PROG
| (GAP) f := function(n) local s, m, c, t, x, a, j; s := 0; m := [1..n]; c := Combinations(m, 2); t := Tuples(m, 2); for x in ConjugacyClasses(SymmetricGroup(n)) do a := Representative(x); j := Length(Cycles(a, m)); s := s+Size(x)*2^j*3^(Length(Cycles(a, t, OnPairs))-Length(Cycles(a, c, OnSets))-j); od; return s/Factorial(n); end;
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CROSSREFS
| Cf. A083667 (labeled antisymmetric relations).
Sequence in context: A153522 A107354 A006118 * A108240 A064606 A066612
Adjacent sequences: A083667 A083668 A083669 * A083671 A083672 A083673
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KEYWORD
| easy,nonn
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AUTHOR
| Goetz Pfeiffer (Goetz.Pfeiffer(AT)nuigalway.ie), May 02 2003
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