

A267324


Number of elements of S_n with strategic pile of size 4.


3



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

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

Table of n, a(n) for n=1..23.
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], 2012017.
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) = (n4)!*(6*binomial(n5,3)+16*binomial(n5,2)+16*binomial(n5,1)) 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(n5)(n^25n+10) Pochhammer[3, n6]];
Array[a, 23] (* JeanFrançois 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 A283546 A297685
Adjacent sequences: A267321 A267322 A267323 * A267325 A267326 A267327


KEYWORD

nonn


AUTHOR

Marion Scheepers, Jan 13 2016


EXTENSIONS

Typo for a(8) corrected by Marion Scheepers, Jun 26 2016


STATUS

approved



