3,2

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).

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.

For references and corresponding links see under A079884

Hugo Pfoertner, FORTRAN program for lexicographic permutation generation.

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)

For n>=3 a(n)=floor(c*n!-(n-3)/2) where c=limit n-->infinity a(n)/n!= 0.261362463274289013838... - Benoit Cloitre (benoit7848c(AT)orange.fr), Jan 20 2003

FORTRAN program available at link

Cf. A000142, partial counts given in A079751, A079755. Number of element comparisons: A079884.

Cf. A038156, A080048.

Sequence in context: A042379 A024394 A095670 this_sequence A121191 A129587 A143551

Adjacent sequences: A079882 A079883 A079884 this_sequence A079886 A079887 A079888

nonn

Hugo Pfoertner (hugo(AT)pfoertner.org), Jan 13 2003