%I #15 Jun 02 2019 11:26:47
%S 2,1,11,14,81,242,1142,4771,29009,127876,805947,4868681,31862753
%N a(n) = number of permutations of {1,...,n} which are twice but not 3-times reformable.
%C Consider a permutation {a1,...,an}; start counting from the beginning: if a1 is not 1, a1 is replaced at the end of an, until we reach the first i such that ai=i in which case ai is removed and the count start from 1 again. The permutation is unreformable if a count of n+1 is reached before all ai are removed. Otherwise, the order of removal of the ai defines the reformed permutation.
%D A. M. Bersani, "Reformed permutations in Mousetrap and its generalizations", preprint MeMoMat 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/~alberto.bersani/mousetrap.html">On the game Mousetrap</a>.
%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 a(4)=2 since 4213->2134->3214, 1432->1423->1234 are the only two permutations that can be reformed twice.
%Y Cf. A007709, A007711, A007712, A067950.
%K nonn
%O 1,1
%A _Robert G. Wilson v_, Jul 05 2000
%E Edited by 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