

A208528


Number of permutations of n>1 having exactly 3 points P on the boundary of their bounding square.


4



0, 4, 16, 72, 384, 2400, 17280, 141120, 1290240, 13063680, 145152000, 1756339200, 22992076800, 323805081600, 4881984307200, 78460462080000, 1339058552832000, 24186745110528000, 460970906812416000, 9245027631071232000, 194632160654131200000
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OFFSET

2,2


COMMENTS

A bounding square for a permutation of n is the square with sides parallel to the coordinate axis containing (1,1) and (n,n), and the set of points P of a permutation p is the set {(k,p(k)) for 0<k<n+1}.
a(n) is the number of permutations of n symbols that 3commute with a transposition (see A233440 for definition): a permutation p of {1,...,n} has exactly three points on the boundary of their bounding square if and only if p 3commutes with transposition (1, n).  Luis Manuel Rivera MartÃnez, Feb 27 2014


LINKS

Vincenzo Librandi, Table of n, a(n) for n = 2..200
E. Deutsch, Permutations and their bounding squares, Math Magazine, 85(1) (2012), p. 63.
Luis Manuel Rivera, Integer sequences and kcommuting permutations, arXiv preprint arXiv:1406.3081, 2014


FORMULA

a(n) = (4*n8) * (n2)!


EXAMPLE

a(3) = 4 because {(1,1),(2,3),(3,2)}, {(1,3),(2,1),(3,2)}, {(1,2),(2,3),(3,1)} and {(1,2),(2,1),(3,3)} each have three points on the bounding square.


MATHEMATICA

Table[(4n8)(n2)!, {n, 2, 10}]


PROG

(Python)
import math
def a(n):
return (4*n8)*math.factorial(n2)


CROSSREFS

Cf. A098916, A208529.
Sequence in context: A217461 A129872 A059371 * A007234 A096244 A030131
Adjacent sequences: A208525 A208526 A208527 * A208529 A208530 A208531


KEYWORD

nonn


AUTHOR

David Nacin, Feb 27 2012


STATUS

approved



