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Search: id:A080049
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| A080049 |
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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 interchange operations in step L4. |
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5
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| 0, 2, 11, 63, 388, 2734, 21893, 197069, 1970726, 21678036, 260136487, 3381774403, 47344841720, 710172625898, 11362762014473, 193166954246169, 3477005176431178, 66063098352192544, 1321261967043851051
(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.
R. J. Ord-Smith: Generation of permutation sequences: Part 1 The Computer Journal Volume 13, Number 2 May 1970. pp. 152-155. See link
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LINKS
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D. E. Knuth, TAOCP Vol. 4, Pre-fascicle 2b (generating all permutations).
R. J. Ord-Smith, Generation of permutation sequences
Hugo Pfoertner, FORTRAN implementation of Knuth's Algorithm L for lexicographic permutation generation.
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FORMULA
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a(2)=0, a(n)=n*a(n-1) + (n-1)*floor[(n-1)/2] c = limit n ->infinity a(n)/n! = 0.5430806.. = (e+1/e)/2-1 a(n) = floor [c*n! - (n-1)/2] for n>=2
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PROGRAM
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FORTRAN program available at Pfoertner link
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CROSSREFS
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Cf. A080047, A080048, A038155, A038156, A056542, A079756.
Sequence in context: A002629 A065928 A114175 this_sequence A126745 A038725 A161947
Adjacent sequences: A080046 A080047 A080048 this_sequence A080050 A080051 A080052
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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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