A092741 Triangle read by rows: T(n,k) is the number of permutations p of [n] in which the length of the longest initial segment avoiding both the 132- and the 321-pattern is equal to k.

1, 0, 2, 0, 2, 4, 0, 8, 9, 7, 0, 40, 45, 24, 11, 0, 240, 270, 144, 50, 16, 0, 1680, 1890, 1008, 350, 90, 22, 0, 13440, 15120, 8064, 2800, 720, 147, 29, 0, 120960, 136080, 72576, 25200, 6480, 1323, 224, 37, 0, 1209600, 1360800, 725760, 252000, 64800, 13230

Offset

1,3

Comments

Row sums are the factorial numbers (A000142).

T(n,2)=n!/3 for n>=3 (A002301). T(n,3)=3n!/8 for n>=4.

Diagonal yields A000124.

Links

Table of n, a(n) for n=1..52.

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) = n!k/[2(k-2)!(k+1)] for k<n; T(n, n) = n(n-1)/2.

Example

T(3,2)=2 because only 132 and 321 satisfy the requirements.

Crossrefs

Cf. A000142, A002301, A000124.

Sequence in context: A317327 A120557 A092594 * A347223 A338227 A350861

Adjacent sequences: A092738 A092739 A092740 * A092742 A092743 A092744

Keyword

nonn,tabl

Author

Emeric Deutsch, Apr 12 2004

Status

approved