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
- 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).
- 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.
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
A028305
Triangle of numbers of permutations eliminating just k cards out of n in game of Mousetrap.
Original entry on oeis.org
1, 0, 1, 1, 0, 1, 2, 2, 0, 2, 9, 6, 3, 0, 6, 44, 31, 19, 11, 0, 15, 265, 180, 105, 54, 32, 0, 84, 1854, 1255, 771, 411, 281, 138, 0, 330, 14833, 9949, 6052, 3583, 2057, 1366, 668, 0, 1812, 133496, 89162, 55340, 32135, 19026, 12685, 6753, 4305, 0, 9978, 1334961, 886837, 547922, 331930, 193538, 117323, 79291, 45536, 25959, 0, 65503
Offset: 0
Triangle begins:
1,
0, 1,
1, 0, 1,
2, 2, 0, 2,
9, 6, 3, 0, 6,
44, 31, 19, 11, 0, 15,
265, 180, 105, 54, 32, 0, 84,
1854, 1255, 771, 411, 281, 138, 0, 330,
...
- 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.
- S. Washburn, T. Marlowe and C. T. Ryan, Discrete Mathematics, Addison-Wesley, 1999, page 326.
- Georg Fischer, Table of n, a(n) for n = 0..107 (terms 36..65 from Martin Renner)
- Arthur Cayley, On the game of Mousetrap, in: 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.
-
A028305:=proc(n)
local P, j, M, K, A, i, K_neu, k, m;
P:=combinat[permute](n):
for j from 0 to n do
M[j]:=0:
od:
for j from 1 to nops(P) do
K:=P[j]:
A:=[]:
for i while nops(K)>0 do
K_neu:=[]:
for k from 1 to n do
m:=nops(K);
if k mod m = 0 then
if K[m]=k then
K_neu:=[seq(K[j],j=1..m-1)];
A:=[op(A),k];
else next;
fi;
else
if K[k mod m]=k then
K_neu:=[seq(K[j],j=(k mod m)+1..m),seq(K[j],j=1..(k mod m)-1)];
A:=[op(A),k];
else next;
fi;
fi;
if nops(K_neu)<>0 then break; fi;
od;
if nops(K_neu)<>0 then
K:=K_neu;
else break;
fi;
od:
M[nops(A)]:=M[nops(A)]+1;
od:
seq(M[j],j=0..n);
end:
# Martin Renner, Sep 03 2015
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
Alberto M. Bersani (bersani(AT)dmmm.uniroma1.it), Feb 09 2007
- 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.
One more term from Alberto M. Bersani (bersani(AT)dmmm.uniroma1.it), Feb 24 2008
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