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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'.
7
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
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
KEYWORD
nonn
AUTHOR
Hugo Pfoertner, Jan 16 2003
EXTENSIONS
Edited and extended by Robert G. Wilson v, Jan 22 2003
STATUS
approved