0,3

Also number of operations needed 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 comparisons required to find j in step L2 (see answer to exercise 5).

Related to number of operations of addition and multiplication to evaluate a determinant of order n by cofactor expansion - see A026243.

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.

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 836

D. E. Knuth, TAOCP Vol. 4, Pre-fascicle 2b (generating all permutations).

Hugo Pfoertner, FORTRAN implementation of Knuth's Algorithm L for lexicographic permutation generation.

Index entries for sequences related to factorial numbers

a(n)=floor[(e-1)*n! ]-1

a(0)=0, a(1)=0, a(n)=n*(a(n-1)+1) for n>1. [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Oct 16 2009]

a(2)=floor[(2.718..-1)*2]-1=3-1=2, a(3)=floor[(2.718..-1)*6]-1=10-1=9

a=1; Table[a=(a-1)*(n+1); Abs[a], {n, 0, 60}] [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Nov 20 2009]

Cf. A038155, A056542, A079884, A079750.

Sequence in context: A038112 A052512 A166554 this_sequence A052846 A056844 A002825

Adjacent sequences: A038153 A038154 A038155 this_sequence A038157 A038158 A038159

nonn,new

N. J. A. Sloane (njas(AT)research.att.com).

Additional comments from Hugo Pfoertner (hugo(AT)pfoertner.org), Jan 24 2003