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A007711 Number of unreformed permutations of {1,...,n}.
(Formerly M3546)
0, 1, 4, 18, 105, 636, 4710, 38508, 352902, 3563297, 39467081, 475326930, 6198134207, 86912048471, 1305146666727, 20897040866280 (list; graph; refs; listen; history; text; internal format)



A. M. Bersani, "Reformed permutations in Mousetrap and its generalizations", preprint MeMoMat n. 15/2005.

R. K. Guy and R. J. Nowakowski, "Mousetrap," in D. Miklos, V. T. Sos and T. Szonyi, eds., Combinatorics, Paul Erdős is Eighty. Bolyai Society Math. Studies, Vol. 1, pp. 193-206, 1993.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).


Table of n, a(n) for n=1..16.

A. M. Bersani, On the game Mousetrap.

A. M. Bersani, Reformed Permutations in mousetrap and its generalizations, INTEGERS, 10 (2010), #G01.

R. K. Guy and R. J. Nowakowski, Mousetrap, Preprint, Feb 10 1993 [Annotated scanned copy]

R. K. Guy and R. J. Nowakowski, Mousetrap, Amer. Math. Monthly, 101 (1994), 1007-1010.


a(n) = n! - A007709(n). - Sean A. Irvine, Jan 17 2018


For n=3, the 4 unreformed permutations are 123, 231, 312, 213, so a(3)=4. Also 132->123, 321->213 are reformable.


Cf. A007709, A007712, A055459, A067950.

Sequence in context: A316186 A231274 A051827 * A321278 A020114 A009597

Adjacent sequences:  A007708 A007709 A007710 * A007712 A007713 A007714




N. J. A. Sloane


More terms from Kok Seng Chua (chuaks(AT)ihpc.nus.edu.sg), Mar 06 2002

2 more terms from Alberto M. Bersani (bersani(AT)dmmm.uniroma1.it), Feb 07 2007

One more term from Alberto M. Bersani (bersani(AT)dmmm.uniroma1.it), Feb 24 2008

a(1) corrected by Joerg Arndt, Dec 24 2014



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Last modified January 16 03:30 EST 2019. Contains 319184 sequences. (Running on oeis4.)