A079751 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 cases where the j search loop runs beyond j=n-3.

0, 1, 6, 37, 260, 2081, 18730, 187301, 2060312, 24723745, 321408686, 4499721605, 67495824076, 1079933185217, 18358864148690, 330459554676421, 6278731538852000, 125574630777040001, 2637067246317840022, 58015479418992480485, 1334356026636827051156

Offset

3,3

Comments

The asymptotic value for large n is 0.051615...*n! = (e - 8/3)*n!. See also comment for A079884.

References

See under A079884.

Links

Table of n, a(n) for n=3..23.

Hugo Pfoertner, FORTRAN program for lexicographic permutation generation.

Formula

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

For n >= 3, a(n) = floor(c*n!) where c = lim_{n->infinity} a(n)/n! = 0.05161516179237856869. - Benoit Cloitre

a(n) = Sum_{j=4..n} (n-j)! * binomial(n,j). - Zerinvary Lajos, Jul 31 2006

E.g.f.: (exp(x) - Sum_{k=0..3} x^k/k!) / (1 - x). - Ilya Gutkovskiy, Jun 26 2022

Maple

a:=n->sum((n-j)!*binomial(n, j), j=4..n): seq(a(n), n=3..25); # Zerinvary Lajos, Jul 31 2006

Mathematica

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

Prog

FORTRAN program available at link

Crossrefs

Cf. A079885, A079750, A079752, A079753, A079754, A079755, A079756.

Sequence in context: A192238 A140712 A362094 * A088312 A012364 A012719

Adjacent sequences: A079748 A079749 A079750 * A079752 A079753 A079754

Keyword

easy,nonn

Author

Hugo Pfoertner, Jan 14 2003

Extensions

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

Status

approved