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A080047
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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.
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5
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0, 1, 7, 41, 256, 1807, 14477, 130321, 1303246, 14335751, 172029067, 2236377937, 31309291196, 469639368031, 7514229888601, 127741908106337, 2299354345914202, 43687732572369991, 873754651447399991
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OFFSET
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2,3
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REFERENCES
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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.
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LINKS
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FORMULA
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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
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MATHEMATICA
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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 *)
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PROG
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FORTRAN program available at Pfoertner link.
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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