

A267324


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


4



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

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], 20142017.


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]];


CROSSREFS

Cf. A267323 gives the corresponding sequence for strategic piles of size 3, A267391 for size 5, and A281259 for size 6.


KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



