A079753 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 total executions of step L3.1'.

0, 3, 21, 136, 967, 7757, 69841, 698446, 7682951, 92195467, 1198541137, 16779575996, 251693640031, 4027098240601, 68460670090337, 1232292061626202, 23413549170897991, 468270983417959991, 9833690651777160001

Offset

3,2

Comments

The asymptotic value for large n is 0.19247...*n! = (e/2-7/6)*n!. See also comment for A079884.

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-1)*(n-2)/2 for n>=4 a(n) = A079752(n) + A079754(n)

For n>=3, a(n)=floor(c*n!-(n-1)/2) where c=limit n-->infinity a(n)/n!= 0.192474247562855951... - Benoit Cloitre, Jan 20 2003

Mathematica

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

Prog

FORTRAN program available at link

Crossrefs

Cf. A079884, A079750, A079751, A079752, A079754, A079755, A079756.

Sequence in context: A125701 A124812 A141041 * A346935 A137969 A303349

Adjacent sequences: A079750 A079751 A079752 * A079754 A079755 A079756

Keyword

nonn

Author

Hugo Pfoertner, Jan 16 2003

Extensions

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

Status

approved