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A079755
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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 loop repetitions in reversal step.
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8
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0, 3, 23, 148, 1054, 8453, 76109, 761126, 8372436, 100469287, 1306100803, 18285411320, 274281169898, 4388498718473, 74604478214169, 1342880607855178, 25514731549248544, 510294630984971051
(list; graph; refs; listen; history; internal format)
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OFFSET
| 3,2
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COMMENTS
| The asymptotic value for large n is 0.20975...*n! = (e+1/e-8/3)/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 lexicogaphic permutation generation
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FORMULA
| a(3)=0, a(n) = n * a(n-1) + (n-1)*floor((n-1)/2) for n>=4.
a(n)=floor(c*n!-(n-1)/2) for n>4, where c=lim n -> infinity a(n)/n!= 0.209747301481910445... - Benoit Cloitre (benoit7848c(AT)orange.fr), Jan 19 2003
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MATHEMATICA
| a[3] = 0; a[n_] := n*a[n - 1] + (n - 1)*Floor[(n - 1)/2]; 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, A079756, A079885.
Sequence in context: A089950 A198797 A057835 * A197176 A006184 A164536
Adjacent sequences: A079752 A079753 A079754 * A079756 A079757 A079758
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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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