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

1,1

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.

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

Table of n, a(n) for n=1..13.

A. M. Bersani, On the game Mousetrap.

R. K. Guy and R. J. Nowakowski, Mousetrap Amer. Math. Monthly, 101 (1994), 1007-1010.

Example

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

Crossrefs

Cf. A007709, A007711, A007712, A067950.

Sequence in context: A305711 A158352 A158354 * A080958 A138351 A120293

Adjacent sequences: A055456 A055457 A055458 * A055460 A055461 A055462

Keyword

nonn

Author

Robert G. Wilson v, Jul 05 2000

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

Status

approved