|
Search: id:A092594
|
|
|
| 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. |
|
+0
1
|
|
| 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
(list; table; graph; listen)
|
|
|
OFFSET
|
1,3
|
|
|
COMMENT
|
Row sums are the factorial numbers (A000142). T(n,2)=n!/3 for n>=3 and T(n,3)=n!/3 for n>=4 (A002301).
|
|
REFERENCES
|
E. Deutsch and W. P. Johnson, Create your own permutation statistic, 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).
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
|
Cf. A000142, A002301.
Adjacent sequences: A092591 A092592 A092593 this_sequence A092595 A092596 A092597
Sequence in context: A137320 A071961 A120557 this_sequence A092741 A037036 A055947
|
|
KEYWORD
|
nonn,tabl
|
|
AUTHOR
|
Emeric Deutsch (deutsch(AT)duke.poly.edu) and Warren P. Johnson (wjohnson(AT)bates.edu), Apr 10 2004
|
|
|
Search completed in 0.002 seconds
|
