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A267324
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Number of elements of S_n with strategic pile of size 4.
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4
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0, 0, 0, 0, 0, 32, 288, 2448, 22080, 216000, 2298240, 26530560, 330946560, 4441651200, 63866880000, 980037273600, 15990989414400, 276529539686400, 5052853757952000, 97290972979200000, 1969085601939456000, 41794695550992384000, 928395406320205824000
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OFFSET
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1,6
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COMMENTS
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Strategic pile is defined in A267323.
The formula given below is a specific instance of the formula that will appear in "Quantifying CDS Sortability of Permutations Using Strategic Piles", see link. - Marisa Gaetz, Jan 18 2017
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LINKS
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K. L. M. Adamyk, E. Holmes, G. R. Mayfield, D. J. Moritz, M. Scheepers, B. E. Tenner, H. C. Wauck, Sorting Permutations: Games, Genomes, and Cycles, arXiv:1410.2353 [math.CO], 2014-2017.
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FORMULA
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a(n) = (n-4)!*(6*binomial(n-5,3) + 16*binomial(n-5,2) + 16*binomial(n-5,1)) for n>5. - Marisa Gaetz, Jan 18 2017
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EXAMPLE
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P = [6,4,2,5,3,1] has strategic pile of size 4: The composition of cycles (0,1,3,5,2,4,6)(0,1,2,3,4,5,6) is (0,3,6,1,4,2,5) = (6,1,4,2,5,0,3) and thus the strategic pile of P is {1,2,4,5}.
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MATHEMATICA
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a[n_] := If[n<6, 0, 2(n-5)(n^2-5n+10) Pochhammer[3, n-6]];
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CROSSREFS
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Cf. A267323 gives the corresponding sequence for strategic piles of size 3, A267391 for size 5, and A281259 for size 6.
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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