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Number of once reformable permutations of {1,2,...,n}.
(Formerly M1283)
5

%I M1283 #20 Jun 06 2019 05:51:32

%S 1,2,4,14,72,316,1730,9728,64330,444890,3645441,28758111,265434293,

%T 2522822881,25717118338

%N Number of once reformable permutations of {1,2,...,n}.

%D A. M. Bersani, "Reformed permutations in Mousetrap and its generalizations", preprint MeMoMat, No. 15, 2005.

%D R. K. Guy, Unsolved Problems Number Theory, Section E37.

%D 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.

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

%H A. M. Bersani, <a href="http://www.dmmm.uniroma1.it/~alberto.bersani/mousetrap.html">On the game Mousetrap</a>.

%H R. K. Guy and R. J. Nowakowski, <a href="/A002467/a002467_1.pdf">Mousetrap</a>, Preprint, Feb 10 1993 [Annotated scanned copy].

%H R. K. Guy and R. J. Nowakowski, <a href="https://www.jstor.org/stable/2975171">Mousetrap</a> Amer. Math. Monthly, 101 (1994), 1007-1010.

%e For n=3, 123, 312, 231, 213 are unreformed but 132->123, 321->213 so a(3)=2.

%Y Cf. A007709, A007711, A055459, A067950.

%K nonn,nice,more

%O 2,2

%A _N. J. A. Sloane_

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

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

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