A281259 - OEIS

A281259

Number of elements of S_n with strategic pile of size 6.

0, 0, 0, 0, 0, 0, 0, 1080, 12960, 143424, 1641600, 19915200, 257644800, 3556224000, 52289556480, 817133184000, 13536585216000, 237105792000000, 4380335511552000, 85148431867699200, 1737742314147840000, 37156364106301440000, 830772012055265280000

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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

Table of n, a(n) for n=1..23.

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

Adjacent sequences: A281256 A281257 A281258 * A281260 A281261 A281262

KEYWORD

nonn

AUTHOR

Marisa Gaetz, Jan 18 2017

STATUS

approved