OFFSET
0,7
COMMENTS
Triangle T(n,k), 0 <= k <= n
REFERENCES
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.
LINKS
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.
EXAMPLE
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,
...
MAPLE
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
CROSSREFS
KEYWORD
AUTHOR
EXTENSIONS
a(36)-a(65) from Martin Renner, Sep 02 2015
STATUS
approved