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A079756
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Operation count to create all permutations of n distinct elements using the "streamlined" version of Algorithm L (lexicographic permutation generation) from Knuth's The Art of Computer Programming, Vol. 4, chapter 7.2.1.2. Sequence gives number of interchanges in reversal step.
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8
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0, 0, 4, 29, 215, 1734, 15630, 156327, 1719637, 20635688, 268264004, 3755696121, 56335441899, 901367070474, 15323240198170, 275818323567179, 5240548147776545, 104810962955531052, 2201030222066152272
(list; graph; refs; listen; history; internal format)
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OFFSET
| 3,3
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COMMENTS
| The asymptotic value for large n is 0.04308...*n! = (e+1/e-3)/2 * n! See also comment for A079884.
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REFERENCES
| See under A079884
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LINKS
| Hugo Pfoertner, FORTRAN program for lexicographic permutation generation
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FORMULA
| a(3)=0, a(4)=0, a(n) = n*a(n-1) + (n-1)*(floor((n-1)/2)-1) for n>=5.
For n>=3, a(n)=floor(c*n!-(n-3)/2) where c=lim n-->infinity a(n)/n!= 0.04308063481524377... - Benoit Cloitre (benoit7848c(AT)orange.fr), Jan 19 2003
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MATHEMATICA
| a[3] = 0; a[4] = 0; a[n_] := n*a[n - 1] + (n - 1)*(Floor[(n - 1)/2] - 1); Table[a[n ], {n, 3, 21}]
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PROG
| FORTRAN program available at link
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CROSSREFS
| Cf. A079884, A079750, A079751, A079752, A079753, A079754, A079755.
Sequence in context: A100022 A001883 A135429 * A087809 A140526 A151343
Adjacent sequences: A079753 A079754 A079755 * A079757 A079758 A079759
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KEYWORD
| nonn
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AUTHOR
| Hugo Pfoertner (hugo(AT)pfoertner.org), Jan 16 2003
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EXTENSIONS
| More terms from Benoit Cloitre (benoit7848c(AT)orange.fr) and Robert G. Wilson v (rgwv(AT)rgwv.com), Jan 19 2003
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