OFFSET
1,3
COMMENTS
LINKS
E. Deutsch and W. P. Johnson, Create your own permutation statistics, Math. Mag., 77, 130-134, 2004.
R. Simion and F. W. Schmidt, Restricted permutations, European J. Combin., 6, 383-406, 1985.
FORMULA
T(n, k) = (k-1)*n!*2^(k-1)*/(k+1)! for k<n; T(n, n)=2^(n-1).
EXAMPLE
T(4,3)=8 because 1243, 1342, 2143, 2341, 3142, 3241, 4132 and 4231 are the only permutations of [4] in which the length of the longest initial segment avoiding both the 132- and the 231-pattern is equal to 3 (i.e. the first three entries contain neither the 132- nor the 231-pattern but all four of them contain at least one of these two patterns).
Triangle starts:
1;
0,2;
0,2,4;
0,8,8,8;
0,40,40,24,16;
0,240,240,144,64,32;
0,1680,1680,1008,448,160,64;
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Emeric Deutsch and Warren P. Johnson (wjohnson(AT)bates.edu), Apr 10 2004
STATUS
approved