cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-5 of 5 results.

A007709 Number of winning (or reformed) decks at Mousetrap.

Original entry on oeis.org

1, 1, 2, 6, 15, 84, 330, 1812, 9978, 65503, 449719, 3674670, 28886593, 266242729, 2527701273, 25749021720
Offset: 1

Views

Author

N. J. A. Sloane

Keywords

References

  • A. M. Bersani, "Reformed permutations in Mousetrap and its generalizations," Preprint Me.Mo.Mat. n. 15/2005.
  • R. K. Guy, Unsolved Problems Number Theory, E37.
  • 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.
  • N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

  • A. M. Bersani, On the game Mousetrap.
  • R. K. Guy and R. J. Nowakowski, Mousetrap, Preprint, Feb 10 1993 [Annotated scanned copy]
  • R. K. Guy and R. J. Nowakowski, Mousetrap Amer. Math. Monthly, 101 (1994), 1007-1010.

Crossrefs

Cf. A007710, A007711, A007712, A055459, A067950.

Extensions

Better description and more terms from Alberto M. Bersani (bersani(AT)dmmm.uniroma1.it), Feb 09 2007
One more term from Alberto M. Bersani (bersani(AT)dmmm.uniroma1.it), Feb 24 2008

A007711 Number of unreformed permutations of {1,...,n}.

Original entry on oeis.org

0, 1, 4, 18, 105, 636, 4710, 38508, 352902, 3563297, 39467081, 475326930, 6198134207, 86912048471, 1305146666727, 20897040866280
Offset: 1

Views

Author

N. J. A. Sloane

Keywords

Examples

			For n=3, the 4 unreformed permutations are 123, 231, 312, 213, so a(3)=4. Also 132->123, 321->213 are reformable.

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.
  • N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Crossrefs

Cf. A007709, A007712, A055459, A067950.

Formula

a(n) = n! - A007709(n). - Sean A. Irvine, Jan 17 2018

Extensions

More terms from 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
a(1) corrected by Joerg Arndt, Dec 24 2014

A007712 Number of once reformable permutations of {1,2,...,n}.

Original entry on oeis.org

1, 2, 4, 14, 72, 316, 1730, 9728, 64330, 444890, 3645441, 28758111, 265434293, 2522822881, 25717118338
Offset: 2

Views

Author

N. J. A. Sloane

Keywords

Examples

			For n=3, 123, 312, 231, 213 are unreformed but 132->123, 321->213 so a(3)=2.

References

  • A. M. Bersani, "Reformed permutations in Mousetrap and its generalizations", preprint MeMoMat, No. 15, 2005.
  • R. K. Guy, Unsolved Problems Number Theory, Section E37.
  • 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.
  • N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

  • A. M. Bersani, On the game Mousetrap.
  • R. K. Guy and R. J. Nowakowski, Mousetrap, Preprint, Feb 10 1993 [Annotated scanned copy].
  • R. K. Guy and R. J. Nowakowski, Mousetrap Amer. Math. Monthly, 101 (1994), 1007-1010.

Crossrefs

Cf. A007709, A007711, A055459, A067950.

Extensions

More terms from 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

A067950 a(n) = number of 3-times (but not 4-times) reformable permutation of {1,...,n}.

Original entry on oeis.org

1, 0, 1, 8, 31, 56, 219, 605, 2485, 9697, 40571
Offset: 6

Views

Author

Kok Seng Chua (chuaks(AT)ihpc.nus.edu.sg), Mar 06 2002

Keywords

Examples

			a(6)=1, 165342->132564->125346->136524.

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

Crossrefs

Cf. A007709, A007711, A007712, A055459.

Extensions

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

A127966 a(n) = number of 4-times (but not 5-times) reformable permutation of {1,...,n}.

Original entry on oeis.org

2, 1, 1, 4, 14, 57
Offset: 11

Views

Author

Alberto M. Bersani (bersani(AT)dmmm.uniroma1.it), Feb 09 2007

Keywords

Comments

For n=16 we have the first example of a 5-reformed (but not 6-reformed) permutation: 1, 16, 12, 15, 6, 8, 14, 10, 9, 3, 4, 11, 13, 2, 7, 5 - Alberto M. Bersani (bersani(AT)dmmm.uniroma1.it), Feb 24 2008

References

  • A. M. Bersani, ``Reformed permutations in Mousetrap and its generalizations,'' Preprint Me.Mo.Mat. 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

Crossrefs

Cf. A007709, A007710, A007711, A007712, A055459, A067950.

Extensions

One more term from Alberto M. Bersani (bersani(AT)dmmm.uniroma1.it), Feb 24 2008
Showing 1-5 of 5 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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