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A055459
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a(n) = number of permutations of {1,...,n} which are twice but not 3-times reformable.
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5
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2, 1, 11, 14, 81, 242, 1142, 4771, 29009, 127876, 805947, 4868681, 31862753
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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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.
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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 Erdos is Eighty. Bolyai Society Math. Studies, Vol. 1, pp. 193-206, 1993.
R. K. Guy and R. J. Nowakowski, ``Mousetrap,'' Amer. Math. Monthly, 101 (1994), 1007-1010.
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LINKS
| A. M. Bersani, On the game Mousetrap.
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EXAMPLE
| a(4)=2 since 4213->2134->3214, 1432->1423->1234 are the only two permutations that can be reformed twice.
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CROSSREFS
| Cf. A007709, A007711, A007712, A067950.
Sequence in context: A088587 A158352 A158354 * A080958 A138351 A120293
Adjacent sequences: A055456 A055457 A055458 * A055460 A055461 A055462
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KEYWORD
| nonn
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AUTHOR
| Robert G. Wilson v (rgwv(AT)rgwv.com), Jul 05 2000
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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
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