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A080049 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. 4
0, 2, 11, 63, 388, 2734, 21893, 197069, 1970726, 21678036, 260136487, 3381774403, 47344841720, 710172625898, 11362762014473, 193166954246169, 3477005176431178, 66063098352192544, 1321261967043851051 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,2

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.

LINKS

Table of n, a(n) for n=2..20.

D. E. Knuth, TAOCP Vol. 4, Pre-fascicle 2b (generating all permutations).

R. J. Ord-Smith, Generation of permutation sequences: Part 1, Computer J., 13 (1970), 151-155.

Hugo Pfoertner, FORTRAN implementation of Knuth's Algorithm L for lexicographic permutation generation.

FORMULA

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.

PROG

FORTRAN program available at Pfoertner link

CROSSREFS

Cf. A080047, A080048, A038155, A038156, A056542, A079756.

Sequence in context: A065928 A188648 A114175 * A126745 A179120 A038725

Adjacent sequences:  A080046 A080047 A080048 * A080050 A080051 A080052

KEYWORD

nonn

AUTHOR

Hugo Pfoertner, Jan 24 2003

STATUS

approved

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Last modified May 29 10:41 EDT 2020. Contains 334699 sequences. (Running on oeis4.)