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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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4
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0, 2, 11, 63, 388, 2734, 21893, 197069, 1970726, 21678036, 260136487, 3381774403, 47344841720, 710172625898, 11362762014473, 193166954246169, 3477005176431178, 66063098352192544, 1321261967043851051
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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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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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PROG
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FORTRAN program available at Pfoertner link
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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