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a(n) = number of 4-times (but not 5-times) reformable permutation of {1,...,n}.
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%I #6 Sep 29 2017 06:09:42

%S 2,1,1,4,14,57

%N a(n) = number of 4-times (but not 5-times) reformable permutation of {1,...,n}.

%C For n=16 we have the first example of a 5-reformed (but not 6-reformed) permutation: 1, 16, 12, 15, 6, 8, 14, 10, 9, 3, 4, 11, 13, 2, 7, 5 - Alberto M. Bersani (bersani(AT)dmmm.uniroma1.it), Feb 24 2008

%D A. M. Bersani, ``Reformed permutations in Mousetrap and its generalizations,'' Preprint Me.Mo.Mat. n. 15/2005.

%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.

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

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

%Y Cf. A007709, A007710, A007711, A007712, A055459, A067950.

%K nonn,more

%O 11,1

%A Alberto M. Bersani (bersani(AT)dmmm.uniroma1.it), Feb 09 2007

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