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A267324 Number of elements of S_n with strategic pile of size 4. 4
0, 0, 0, 0, 0, 32, 288, 2448, 22080, 216000, 2298240, 26530560, 330946560, 4441651200, 63866880000, 980037273600, 15990989414400, 276529539686400, 5052853757952000, 97290972979200000, 1969085601939456000, 41794695550992384000, 928395406320205824000 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,6
COMMENTS
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
LINKS
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.
Marisa Gaetz, Bethany Flanagan, Marion Scheepers, Meghan Shanks, Quantifying CDS Sortability of Permutations by Strategic Pile Size, arXiv:1811.11937 [math.CO], 2018.
M. Gaetz, B. Molokach, M. Scheepers, and M. Shanks, Quantifying CDS Sortability of Permutations Using Strategic Piles
FORMULA
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
EXAMPLE
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}.
MATHEMATICA
a[n_] := If[n<6, 0, 2(n-5)(n^2-5n+10) Pochhammer[3, n-6]];
Array[a, 23] (* Jean-François Alcover, Dec 12 2018 *)
CROSSREFS
Cf. A267323 gives the corresponding sequence for strategic piles of size 3, A267391 for size 5, and A281259 for size 6.
Sequence in context: A316881 A317609 A251782 * A197523 A337418 A283546
KEYWORD
nonn
AUTHOR
Marion Scheepers, Jan 13 2016
EXTENSIONS
Typo for a(8) corrected by Marion Scheepers, Jun 26 2016
STATUS
approved

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Last modified April 21 04:54 EDT 2024. Contains 371850 sequences. (Running on oeis4.)