A079754 Operation count to create all permutations of n distinct elements using the "streamlined" version of 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 L3.1'.

0, 1, 8, 54, 388, 3119, 28092, 280948, 3090464, 37085613, 482113024, 6749582402, 101243736108, 1619899777819, 27538296223028, 495689332014624, 9418097308277992, 188361946165559993, 3955600869476760024

Offset

3,3

Comments

The asymptotic value for large n is 0.07742...*n! See also comment for A079884.

Lim_{n->infinity} a(n)/n! = 3*e/2 - 4. - Hugo Pfoertner, Sep 02 2017

References

See under A079884

Links

Table of n, a(n) for n=3..21.

Hugo Pfoertner, FORTRAN program for lexicographic permutation generation

Formula

a(3)=0, a(n) = n*a(n-1) + (n-2)*(n-3)/2 for n>=4 a(n) = A079753(n) - A079752(n)

For n>=3 a(n)=floor(c*n!-(n-3)/2) where c=limit n --> infinity a(n)/n!=0.077422742688567853... - Benoit Cloitre, Jan 20 2003

Mathematica

a[3] = 0; a[n_] := n*a[n - 1] + (n - 2)*(n - 3)/2; Table[a[n], {n, 3, 21}]

Prog

FORTRAN program available at link

Crossrefs

Cf. A079884, A079750, A079751, A079752, A079753, A079755, A079756, A196533.

Sequence in context: A201640 A263885 A002775 * A347274 A298985 A142703

Adjacent sequences: A079751 A079752 A079753 * A079755 A079756 A079757

Keyword

nonn

Author

Hugo Pfoertner, Jan 16 2003

Extensions

Edited and extended by Robert G. Wilson v, Jan 22 2003

Status

approved