A092594 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 231-pattern is equal to k.
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, 0, 13440, 13440, 8064, 3584, 1280, 384, 128, 0, 120960, 120960, 72576, 32256, 11520, 3456, 896, 256, 0, 1209600, 1209600, 725760, 322560, 115200, 34560
Offset: 1
Examples
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;
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
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
Comments
Examples
T(3,2)=2 because only 132 and 321 satisfy the requirements.
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) = n!k/[2(k-2)!(k+1)] for k
Comments