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.

0, 2, 11, 63, 388, 2734, 21893, 197069, 1970726, 21678036, 260136487, 3381774403, 47344841720, 710172625898, 11362762014473, 193166954246169, 3477005176431178, 66063098352192544, 1321261967043851051

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 * A370392 A126745 A362799

Adjacent sequences: A080046 A080047 A080048 * A080050 A080051 A080052

Keyword

nonn

Author

Hugo Pfoertner, Jan 24 2003

Status

approved