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Search: id:A080048
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| A080048 |
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Operation count to create all permutations of n distinct elements using 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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6
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| 1, 7, 34, 182, 1107, 7773, 62212, 559948, 5599525, 61594835, 739138086, 9608795202, 134523132919, 2017846993897, 32285551902472, 548854382342168, 9879378882159177, 187708198761024543, 3754163975220491050
(list; graph; listen)
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OFFSET
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2,2
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REFERENCES
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D. E. Knuth: The Art of Computer Programming, Volume 4, Combinatorial Algorithms, Volume 4A, Enumeration and Backtracking. Pre-fascicle 2B, A draft of section 7.2.1.2: Generating all permutations. Available online; see link.
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LINKS
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D. E. Knuth, TAOCP Vol. 4, Pre-fascicle 2b (generating all permutations).
FORTRAN implementation of Knuth's Algorithms L for lexicographic permutation generation.
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FORMULA
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a(2)=1, a(n)=n*a(n-1) + (n-1)*floor[(n+1)/2] for n>=3. c = limit n --> infinity a(n)/n! = 1.54308063481524377826 = (e+1/e)/2 a(n) = floor [c*n!-(n+1)/2] for n>=2.
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PROGRAM
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FORTRAN program available at link.
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CROSSREFS
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Cf. A038155, A038156, A056542, A080047, A080049, A079755.
Sequence in context: A124466 A055271 A027209 this_sequence A027233 A117650 A144038
Adjacent sequences: A080045 A080046 A080047 this_sequence A080049 A080050 A080051
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KEYWORD
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nonn
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AUTHOR
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Hugo Pfoertner (hugo(AT)pfoertner.org), Jan 24 2003
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