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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 (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

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], (16-December-2014)

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}.

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: A223904 A122103 A009526 * A197523 A283546 A250563

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

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Last modified November 18 00:38 EST 2017. Contains 294837 sequences.