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

Author

Hugo Pfoertner, Jan 16 2003

Keywords

• nonn

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

• Hugo Pfoertner, FORTRAN program for lexicographic permutation generation

Crossrefs

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

Programs

Mathematica

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

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

Extensions

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