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A080047
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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 times l has to be repeatedly decreased in step L3.
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4
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0, 1, 7, 41, 256, 1807, 14477, 130321, 1303246, 14335751, 172029067, 2236377937, 31309291196, 469639368031, 7514229888601, 127741908106337, 2299354345914202, 43687732572369991, 873754651447399991
(list; graph; refs; listen; history; internal format)
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OFFSET
| 2,3
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REFERENCES
| 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
| D. E. Knuth, TAOCP Vol. 4, Pre-fascicle 2b (generating all permutations).
Hugo Pfoertner, FORTRAN implementation of Knuth's Algorithms L for lexicographic permutation generation
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FORMULA
| a(2)=0, a(n) = n*a(n-1)+(n-1)*(n-2)/2 for n>=3 c = limit n--> infinity a(n)/n! = 0.35914091422952261768 = e/2-1, a(n) = floor [c*n! - (n-1)/2] for n>=2
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PROG
| FORTRAN program available at Pfoertner link.
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CROSSREFS
| Cf. A038155, A038156, A056542, A080048, A080049, A079754.
Sequence in context: A108983 A115137 A036730 * A125120 A181441 A146991
Adjacent sequences: A080044 A080045 A080046 * A080048 A080049 A080050
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KEYWORD
| nonn
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AUTHOR
| Hugo Pfoertner (hugo(AT)pfoertner.org), Jan 25 2003
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