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

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