|
| |
|
|
A032351
|
|
Number of permutations of length n which avoid the patterns 2143, 1324 (smooth permutations); or avoid the patterns 1342, 2431; etc.
|
|
3
| |
|
|
1, 1, 2, 6, 22, 88, 366, 1552, 6652, 28696, 124310, 540040, 2350820, 10248248, 44725516, 195354368, 853829272, 3733693872, 16333556838, 71476391800, 312865382004, 1369760107576, 5998008630244, 26268304208032, 115055864102504, 503997820344464, 2207927106851580, 9673223726469136, 42382192892577128, 185702341264971696
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,3
|
|
|
REFERENCES
| Kremer, Darla and Shiu, Wai Chee; Finite transition matrices for permutations avoiding pairs of length four patterns. Discrete Math. 268 (2003), 171-183. MR1983276 (2004b:05006). See Table 1.
R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 2, 1999; see Problem 6.47.
A. Woo and A. Yong, "When is a Schubert variety Gorenstein?", preprint 2004.
|
|
|
LINKS
| Miklos Bona, The permutation classes equinumerous to the smooth class, Electron. J. Combin., 5 (1998), no. 1, Research Paper 31, 12 pp.
M. Bousquet-Melou and S. Butler, Forest-like permutations.
Wikipedia, Permutation classes avoiding two patterns of length 4.
A. Woo and A. Yong, When is a Schubert variety Gorenstein?.
|
|
|
FORMULA
| G.f.: (1-5*x+3*x^2+x^2*sqrt(1-4*x))/(1-6*x+8*x^2-4*x^3)
a(n) = upper left term in n-th power of the following infinite square production matrix:
1, 1, 0, 0, 0, 0,...
1, 2, 1, 0, 0, 0,...
1, 3, 1, 1, 0, 0,...
1, 4, 1, 1, 1, 0,...
1, 5, 1, 1, 1, 1,...
...
- Gary W. Adamson, Jul 11 2011
|
|
|
PROG
| (Pari) x='x+O('x^44) /* that many terms */
gf=(1-5*x+3*x^2+x^2*sqrt(1-4*x))/(1-6*x+8*x^2-4*x^3);
Vec(gf) /* show terms */ /* Joerg Arndt, Apr 20 2011 */
|
|
|
CROSSREFS
| Cf. A053617.
Sequence in context: A165534 A165535 A165536 * A165537 A165538 A165539
Adjacent sequences: A032348 A032349 A032350 * A032352 A032353 A032354
|
|
|
KEYWORD
| nonn,easy,nice,changed
|
|
|
AUTHOR
| Miklos Bona (bona(AT)math.ufl.edu)
|
|
|
EXTENSIONS
| More terms from Erich Friedman (erich.friedman(AT)stetson.edu).
|
| |
|
|
