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A281259
Number of elements of S_n with strategic pile of size 6.
2
0, 0, 0, 0, 0, 0, 0, 1080, 12960, 143424, 1641600, 19915200, 257644800, 3556224000, 52289556480, 817133184000, 13536585216000, 237105792000000, 4380335511552000, 85148431867699200, 1737742314147840000, 37156364106301440000, 830772012055265280000
OFFSET
1,8
COMMENTS
Strategic pile is as 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.
LINKS
M. Gaetz, B. Molokach, M. Scheepers, and M. Shanks, Quantifying CDS Sortability of Permutations Using Strategic Piles
Marisa Gaetz, Bethany Flanagan, Marion Scheepers, Meghan Shanks, Quantifying CDS Sortability of Permutations by Strategic Pile Size, arXiv:1811.11937 [math.CO], 2018.
FORMULA
a(n) = (n-6)!*(120*binomial(n-7,5) + 576*binomial(n-7,4) + 1116*binomial(n-7,3) + 1080*binomial(n-7,2) + 540*binomial(n-7,1)) for n>7.
EXAMPLE
The permutation P = [3,5,1,8,6,2,7,4] has strategic pile of size 6. This can be found by the following cycle composition: (0,4,7,2,6,8,1,5,3)(0,1,2,3,4,5,6,7,8)=(0,5,8,4,3,7,1,6,2). Therefore, the strategic pile of P is {4,3,7,1,6,2}.
CROSSREFS
Cf. A267323 (size 3), A267324 (size 4), A267391 (size 5).
Sequence in context: A179688 A159210 A250538 * A251795 A092135 A077740
KEYWORD
nonn
AUTHOR
Marisa Gaetz, Jan 18 2017
STATUS
approved