A079750 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 comparisons required to find j in step L2.2'.

0, 4, 25, 156, 1099, 8800, 79209, 792100, 8713111, 104557344, 1359245485, 19029436804, 285441552075, 4567064833216, 77640102164689, 1397521838964420, 26552914940323999, 531058298806480000, 11152224274936080021

Offset: 3

Author

Hugo Pfoertner, Jan 14 2003

Keywords

• easy
• nonn

Comments

The asymptotic value for large n is 0.21828...*n! See also comment for A079884

References

• See under A079884

Links

• Hugo Pfoertner, FORTRAN program for lexicographic permutation generation.

Crossrefs

Cf. A079884, A079751, A079752, A079753, A079754, A079755, A079756.

Programs

Fortran

c Program available at link.

Maple

a:=n->sum((n+1)!/j!,j=3..n): seq(a(n), n=2..20); # Zerinvary Lajos, Oct 20 2006

Mathematica

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

Formula

a(3)=0, a(n) = n * a(n-1) + n for n >= 4.

a(n) = Sum_{j=3..n} (n+1)!/j!. - Zerinvary Lajos, Oct 20 2006

For n >= 3, a(n) = floor((e - 5/2)*n! - 1/2). - Benoit Cloitre, Aug 03 2007

Extensions

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