A080048 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 loop repetitions in reversal step.

1, 7, 34, 182, 1107, 7773, 62212, 559948, 5599525, 61594835, 739138086, 9608795202, 134523132919, 2017846993897, 32285551902472, 548854382342168, 9879378882159177, 187708198761024543, 3754163975220491050

Offset: 2

Author

Hugo Pfoertner, Jan 24 2003

Keywords

• nonn
• changed

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

• D. E. Knuth, TAOCP Vol. 4, Pre-fascicle 2b (generating all permutations).
• FORTRAN implementation of Knuth's Algorithms L for lexicographic permutation generation.

Crossrefs

Cf. A038155, A038156, A056542, A080047, A080049, A079755.

Programs

Fortran

! Program available at link.

Formula

a(2)=1, a(n)=n*a(n-1) + (n-1)*floor[(n+1)/2] for n>=3.

c = limit n --> infinity a(n)/n! = 1.54308063481524377826 = (e+1/e)/2, a(n) = floor [c*n!-(n+1)/2] for n>=2.