%I A055459
%S A055459 2,1,11,14,81,242,1142,4771,29009,127876,805947,4868681,31862753
%N A055459 a(n) = number of permutations of {1,...,n} which are twice but not 3-times 
               reformable.
%C A055459 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 A055459 A. M. Bersani, "Reformed permutations in Mousetrap and its generalizations", 
               preprint MeMoMat n. 15/2005.
%D A055459 R. K. Guy and R. J. Nowakowski, ``Mousetrap,'' in D. Miklos, V.T. Sos 
               and T. Szonyi, eds., Combinatorics, Paul Erdos is Eighty. Bolyai 
               Society Math. Studies, Vol. 1, pp. 193-206, 1993.
%D A055459 R. K. Guy and R. J. Nowakowski, ``Mousetrap,'' Amer. Math. Monthly, 101 
               (1994), 1007-1010.
%H A055459 A. M. Bersani, <a href="http://www.dmmm.uniroma1.it/~bersani/mousetrap.html">
               On the game Mousetrap</a>.
%e A055459 a(4)=2 since 4213->2134->3214, 1432->1423->1234 are the only two permutations 
               that can be reformed twice.
%Y A055459 Cf. A007709, A007711, A007712, A067950.
%Y A055459 Sequence in context: A088587 A158352 A158354 this_sequence A080958 A138351 
               A120293
%Y A055459 Adjacent sequences: A055456 A055457 A055458 this_sequence A055460 A055461 
               A055462
%K A055459 nonn
%O A055459 1,1
%A A055459 Robert G. Wilson v (rgwv(AT)rgwv.com), Jul 05 2000
%E A055459 Edited by Kok Seng Chua (chuaks(AT)ihpc.nus.edu.sg), Mar 06 2002
%E A055459 2 more terms from Alberto M. Bersani (bersani(AT)dmmm.uniroma1.it), Feb 
               07 2007
%E A055459 One more term from Alberto M. Bersani (bersani(AT)dmmm.uniroma1.it), 
               Feb 24 2008