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A079756 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 interchanges in reversal step. 9
0, 0, 4, 29, 215, 1734, 15630, 156327, 1719637, 20635688, 268264004, 3755696121, 56335441899, 901367070474, 15323240198170, 275818323567179, 5240548147776545, 104810962955531052, 2201030222066152272 (list; graph; refs; listen; history; text; internal format)
OFFSET

3,3

COMMENTS

The asymptotic value for large n is 0.04308...*n! = (e+1/e-3)/2 * n! See also comment for A079884.

REFERENCES

See under A079884

LINKS

Indranil Ghosh, Table of n, a(n) for n = 3..101

Hugo Pfoertner, FORTRAN program for lexicographic permutation generation

FORMULA

a(3)=0, a(4)=0, a(n) = n*a(n-1) + (n-1)*(floor((n-1)/2)-1) for n>=5.

For n>=3, a(n) = floor(c*n!-(n-3)/2) where c = lim_{n->infinity} a(n)/n! = 0.04308063481524377... - Benoit Cloitre, Jan 19 2003

Recurrence: (n-5)*(n-3)*(n-2)*a(n) = (n-3)*(n^3 - 7*n^2 + 11*n - 1)*a(n-1) - (n-1)*(2*n - 5)*a(n-2) - (n-4)*(n-2)^2*(n-1)*a(n-3). - Vaclav Kotesovec, Mar 16 2014

MATHEMATICA

a[3] = 0; a[4] = 0; a[n_] := n*a[n - 1] + (n - 1)*(Floor[(n - 1)/2] - 1); Table[a[n ], {n, 3, 21}]

PROG

FORTRAN program available at link

(Python)

l=[0, 0, 0, 0, 0]

for n in range(5, 22):

    l.append(n*l[n - 1] + (n - 1)*((n - 1)//2 - 1))

print(l[3:]) # Indranil Ghosh, Jul 18 2017

CROSSREFS

Cf. A079884, A079750, A079751, A079752, A079753, A079754, A079755.

Sequence in context: A001883 A281600 A135429 * A344098 A221415 A087809

Adjacent sequences:  A079753 A079754 A079755 * A079757 A079758 A079759

KEYWORD

nonn

AUTHOR

Hugo Pfoertner, Jan 16 2003

EXTENSIONS

More terms from Benoit Cloitre and Robert G. Wilson v, Jan 19 2003

STATUS

approved

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Last modified May 14 18:54 EDT 2021. Contains 343900 sequences. (Running on oeis4.)