A055459 a(n) = number of permutations of {1,...,n} which are twice but not 3-times reformable.

2, 1, 11, 14, 81, 242, 1142, 4771, 29009, 127876, 805947, 4868681, 31862753

Offset: 1

Author

Robert G. Wilson v, Jul 05 2000

Keywords

• nonn

Comments

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.

Examples

			a(4)=2 since 4213->2134->3214, 1432->1423->1234 are the only two permutations that can be reformed twice.
		

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.

Links

• A. M. Bersani, On the game Mousetrap.
• R. K. Guy and R. J. Nowakowski, Mousetrap Amer. Math. Monthly, 101 (1994), 1007-1010.

Crossrefs

Cf. A007709, A007711, A007712, A067950.

Extensions

Edited by 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