Search: id:A080048
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%I A080048
%S A080048 1,7,34,182,1107,7773,62212,559948,5599525,61594835,739138086,
%T A080048 9608795202,134523132919,2017846993897,32285551902472,548854382342168,
%U A080048 9879378882159177,187708198761024543,3754163975220491050
%N A080048 Operation count to create all permutations of n distinct elements using 
               Algorithm L (lexicographic permutation generation) from Knuth's The 
               Art of Computer Programming, Vol. 4, chapter 7.2.1.2. Sequence gives 
               number of loop repetitions in reversal step.
%D A080048 D. E. Knuth: The Art of Computer Programming, Volume 4, Combinatorial 
               Algorithms, Volume 4A, Enumeration and Backtracking. Pre-fascicle 
               2B, A draft of section 7.2.1.2: Generating all permutations. Available 
               online; see link.
%H A080048 D. E. Knuth, <a href="http://www-cs-faculty.stanford.edu/~knuth/fasc2b.ps.gz">
               TAOCP Vol. 4, Pre-fascicle 2b (generating all permutations)</a>.
%H A080048 <a href="http://www.randomwalk.de/sequences/lpure.txt">FORTRAN implementation 
               of Knuth's Algorithms L for lexicographic permutation generation</
               a>.
%F A080048 a(2)=1, a(n)=n*a(n-1) + (n-1)*floor[(n+1)/2] for n>=3. c = limit n --> 
               infinity a(n)/n! = 1.54308063481524377826 = (e+1/e)/2 a(n) = floor 
               [c*n!-(n+1)/2] for n>=2.
%o A080048 FORTRAN program available at link.
%Y A080048 Cf. A038155, A038156, A056542, A080047, A080049, A079755.
%Y A080048 Sequence in context: A124466 A055271 A027209 this_sequence A027233 A117650 
               A144038
%Y A080048 Adjacent sequences: A080045 A080046 A080047 this_sequence A080049 A080050 
               A080051
%K A080048 nonn
%O A080048 2,2
%A A080048 Hugo Pfoertner (hugo(AT)pfoertner.org), Jan 24 2003

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