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%I #9 Mar 18 2014 09:56:50
%S 0,4,29,185,1314,10534,94839,948427,10432748,125193032,1627509489,
%T 22785132925
%N Number of index tests required 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.
%C The required number of index tests (test for termination and test in the final reversion loop) becomes 0.2613625*n! for large n, if the test for n=3 is excluded. If n=3 is included the additionally required termination test adds n!/6 index comparisons, increasing the number of index comparisons to 0.428029*n! (63.8% more index comparisons).
%C The corresponding number of index tests needed by the "pure" Algorithm L is given by A038156(n)+A080048(n), which is 12.478..*a(n) for large n.
%D For references and corresponding links see under A079884
%H Hugo Pfoertner, <a href="http://www.randomwalk.de/sequences/lpgcount.txt">FORTRAN program for lexicographic permutation generation</a>.
%F a(3)=0, a(n)=n*a(n-1)+1+(n-1)*floor((n-1)/2) for n>=4 a(n) = A079751(n) + A079755(n)
%F For n>=3 a(n)=floor(c*n!-(n-3)/2) where c=limit n-->infinity a(n)/n!= 0.261362463274289013838... - _Benoit Cloitre_, Jan 20 2003
%F In closed form, c = 3*exp(1)/2 + exp(-1)/2 - 4. - _Vaclav Kotesovec_, Mar 18 2014
%o FORTRAN program available at link
%Y Cf. A000142, partial counts given in A079751, A079755. Number of element comparisons: A079884.
%Y Cf. A038156, A080048.
%K nonn
%O 3,2
%A _Hugo Pfoertner_, Jan 13 2003
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