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A007711
Number of unreformed permutations of {1,...,n}.
(Formerly M3546)
5
0, 1, 4, 18, 105, 636, 4710, 38508, 352902, 3563297, 39467081, 475326930, 6198134207, 86912048471, 1305146666727, 20897040866280
OFFSET
1,3
REFERENCES
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).
LINKS
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.
FORMULA
a(n) = n! - A007709(n). - Sean A. Irvine, Jan 17 2018
EXAMPLE
For n=3, the 4 unreformed permutations are 123, 231, 312, 213, so a(3)=4. Also 132->123, 321->213 are reformable.
CROSSREFS
KEYWORD
nonn,more
EXTENSIONS
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
STATUS
approved