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

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

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.

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

Cf. A007709, A007712, A055459, A067950.

Sequence in context: A316186 A231274 A051827 * A321278 A020114 A354015

Adjacent sequences: A007708 A007709 A007710 * A007712 A007713 A007714

Keyword

nonn,more

Author

N. J. A. Sloane

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