A028305 -id:A028305 - cp's OEIS frontend

A007710 From the game of Mousetrap.

Original entry on oeis.org

1, 0, 2, 6, 31, 180, 1255, 9949, 89162, 886837, 9722814, 116236256, 1507191024, 21042127239

Offset: 1

N. J. A. Sloane

nonn

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).

Arthur Cayley, On the game of Mousetrap, Quarterly Journal of Pure and Applied Mathematics 15 (1878), p. 8-10.
R. K. Guy and R. J. Nowakowski, Mousetrap, Preprint, Feb 10 1993 [Annotated scanned copy]
Adolph Steen, Some formulas respecting the game of Mousetrap, Quarterly Journal of Pure and Applied Mathematics 15 (1878), p. 230-241.

Cf. A028305.

a(n) = A028305((1/2)*(n+1)*(n+2)-n+1). - Martin Renner, Sep 03 2015

a(10) from Martin Renner, Sep 02 2015

a(11)-a(14) from Sean A. Irvine, Jan 17 2018

A028306 Triangle read by rows of numbers of permutations eliminating just card k out of n in game of Mousetrap.

Original entry on oeis.org

1, 0, 0, 1, 0, 1, 2, 1, 1, 2, 9, 5, 5, 3, 9, 44, 31, 25, 20, 16, 44, 265, 203, 167, 142, 117, 96, 265, 1854, 1501, 1267, 1075, 932, 791, 675, 1854, 14833, 12449, 10745, 9311, 8241, 7132, 6205, 5413, 14833, 133496, 114955, 101005, 88993, 78607, 70340, 62141

Offset: 0

N. J. A. Sloane

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.

R. K. Guy and R. J. Nowakowski, Mousetrap, Preprint, Feb 10 1993 [Annotated scanned copy]

Diagonals include A000166, A002469. Cf. A028305.

A261867 Triangle T(n, k) read by rows (n >= 1, 1 <= k <= n), where row n gives the lexicographically first permutation of n cards that is a winning (or reformed) deck at Cayley's Mousetrap.

Original entry on oeis.org

1, 1, 2, 1, 3, 2, 1, 2, 4, 3, 1, 2, 5, 3, 4, 1, 2, 4, 3, 6, 5, 1, 2, 3, 7, 6, 5, 4, 1, 2, 3, 5, 8, 4, 6, 7, 1, 2, 3, 4, 8, 5, 7, 9, 6, 1, 2, 3, 4, 6, 9, 8, 7, 10, 5, 1, 2, 3, 4, 6, 7, 5, 11, 8, 10, 9, 1, 2, 3, 4, 5, 8, 10, 6, 12, 9, 11, 7, 1, 2, 3, 4, 5, 6, 9, 12, 7, 10, 13, 11, 8, 1, 2, 3, 4, 5, 6, 10, 9, 14, 13, 8, 11, 12, 7, 1, 2, 3, 4, 5, 6, 8, 9, 12, 7, 14, 10, 15, 13, 11

Offset: 1

Martin Renner, Sep 03 2015

			With four cards in the order 1243 the player will win the first time (out of six times), taking the cards away in the order 1342, i.e., the cards held in hand develop from 1243 -> 243 -> 24 -> 2.
Triangle starts with
1
1, 2
1, 3, 2
1, 2, 4, 3
1, 2, 5, 3, 4
...

Arthur Cayley, On the game of Mousetrap, Quarterly Journal of Pure and Applied Mathematics 15 (1878), pp. 8-10.
Adolph Steen, Some formulas respecting the game of Mousetrap, Quarterly Journal of Pure and Applied Mathematics 15 (1878), pp. 230-241.

Cf. A007709, A028305.

cp's OEIS Frontend

A007710 From the game of Mousetrap.

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A028306 Triangle read by rows of numbers of permutations eliminating just card k out of n in game of Mousetrap.

Views

Author

Keywords

References

Links

Crossrefs

A261867 Triangle T(n, k) read by rows (n >= 1, 1 <= k <= n), where row n gives the lexicographically first permutation of n cards that is a winning (or reformed) deck at Cayley's Mousetrap.

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