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Search: id:A079751
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| A079751 |
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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. |
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+0
9
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| 0, 1, 6, 37, 260, 2081, 18730, 187301, 2060312, 24723745, 321408686, 4499721605, 67495824076, 1079933185217, 18358864148690, 330459554676421, 6278731538852000, 125574630777040001, 2637067246317840022
(list; graph; listen)
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OFFSET
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3,3
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COMMENT
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The asymptotic value for large n is 0.051615...*n! See also comment for A079884
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REFERENCES
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See under A079884
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LINKS
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Hugo Pfoertner, FORTRAN program for lexicographic permutation generation.
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FORMULA
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a(3)=0, a(n) = n * a(n-1) + 1 for n>=4
For n>=3, a(n)=floor(c*n!) where c=limit n->infinity a(n)/n!=0.05161516179237856869 - Ben Cloitre
a:=n->sum((n-j)!*binomial(n,j),j=4..n). - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 31 2006
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MAPLE
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a:=n->sum((n-j)!*binomial(n, j), j=4..n): seq(a(n), n=3..25); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 31 2006
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MATHEMATICA
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a[3] = 0; a[n_] := n*a[n - 1] + 1; Table[a[n], {n, 3, 21}]
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PROGRAM
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FORTRAN program available at link
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CROSSREFS
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Cf. A079885, A079750, A079752, A079753, A079754, A079755, A079756.
Sequence in context: A080954 A073013 A140712 this_sequence A088312 A012364 A012719
Adjacent sequences: A079748 A079749 A079750 this_sequence A079752 A079753 A079754
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KEYWORD
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easy,nonn
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AUTHOR
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Hugo Pfoertner (hugo(AT)pfoertner.org), Jan 14 2003
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EXTENSIONS
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Edited and extended by Robert G. Wilson v (rgwv(AT)rgwv.com), Jan 22 2003
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