A080047 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 times l has to be repeatedly decreased in step L3.

0, 1, 7, 41, 256, 1807, 14477, 130321, 1303246, 14335751, 172029067, 2236377937, 31309291196, 469639368031, 7514229888601, 127741908106337, 2299354345914202, 43687732572369991, 873754651447399991

Offset: 2

Author

Hugo Pfoertner, Jan 25 2003

Keywords

• nonn

References

• 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.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 2..200
• D. E. Knuth, TAOCP Vol. 4, Pre-fascicle 2b (generating all permutations).
• Hugo Pfoertner, FORTRAN implementation of Knuth's Algorithms L for lexicographic permutation generation

Crossrefs

Cf. A038155, A038156, A056542, A080048, A080049, A079754.

Programs

Mathematica

Transpose[NestList[{First[#]+1,(First[#]+1)Last[#]+(First[#](First[#]-1))/2}&, {2,0},20]][[2]] (* Harvey P. Dale, Feb 27 2012 *)
Rest[Rest[CoefficientList[Series[(2-Exp[x]*(x^2-2*x+2))/(2*(x-1)),{x,0,20}],x]*Range[0,20]!]] (* Vaclav Kotesovec, Oct 21 2012 *)

Formula

a(2)=0, a(n) = n*a(n-1)+(n-1)*(n-2)/2 for n>=3 c = limit n--> infinity a(n)/n! = 0.35914091422952261768 = e/2-1, a(n) = floor [c*n! - (n-1)/2] for n>=2

E.g.f.: (2-exp(x)*(x^2-2*x+2))/(2*(x-1)). - Vaclav Kotesovec, Oct 21 2012